Selection of Probability Density Functions (Pdfs) for the ... · decay chains considered in the...

Selection of Probability Density Functions (Pdfs) for the PSA of the

“Initial Defect in the Canister” Reference Model

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POSIVA OY

Olki luoto

FI-27160 EURAJOKI, F INLAND

Phone (02) 8372 31 (nat. ) , (+358-2-) 8372 31 ( int. )

Fax (02) 8372 3809 (nat. ) , (+358-2-) 8372 3809 ( int. )

December 2013

Working Report 2013-61

José Luis Cormenzana

December 2013

Working Reports contain information on work in progress

or pending completion.

José Luis Cormenzana

Working Report 2013-61

Selection of Probability Density Functions (Pdfs) for the PSA of the

“Initial Defect in the Canister” Reference Model

ABSTRACT

In Posiva Oy´s Safety Case “TURVA-2012” the repository system scenarios leading to radionuclide releases have been identified in Formulation of Radionuclide Release Scenarios. Three potential causes of canister failure and radionuclide release are considered: (i) the presence of an initial defect in the copper shell of one canister that penetrates de shell completely, (ii) corrosion of the copper overpack, that occurs more rapidly if buffer density is reduced, e.g. by erosion, (iii) shear movement on fractures intersecting the deposition hole.

All three failure modes are analyzed deterministically in Assessment of Radionuclide Release Scenarios, and for the “initial defect in the canister” reference model a probabilistic sensitivity analysis (PSA) has been carried out.

The main steps of the PSA have been:

- quantification of the uncertainties in the model input parameters through the creation of probability density distributions (PDFs),

- Monte Carlo simulations of the evolution of the system up to 106 years using parameters values sampled from the previous PDFs. Monte Carlo simulations with 10,000 individual calculations (realisations) have been used in the PSA,

- quantification of the uncertainty in the model outputs due to uncertainty in the input parameters (uncertainty analysis), and

- identification of the parameters whose uncertainty have the greatest effect on the uncertainty in the model outputs (sensitivity analysis)

This working report describes the first step of the PSA performed by Posiva; i.e. it presents the input data considered and the process followed to define the probability density functions (PDFs) used in the PSA. For the solubility limits in the canister interior and the distribution coefficients in the buffer and the backfill, there are data available for different groundwater compositions (which accounts for the geochemical uncertainty) and the different sources of uncertainty for a given water composition have been quantified (formal uncertainty). All these data have been used to create Log-Normal distributions for these parameters. The PDFs for the near field and far field flow-related parameters are created using the data in the output file of the groundwater modelling case that corresponds to the hydrogeological boundary conditions predicted for 5,000 AD. For most of the remaining parameters Log-Uniform PDFs are adopted. Log-Uniform distributions assign the same probability to all the orders of magnitude covered by the range of values, and allow sampling the whole range of uncertainty of the input parameters with a reasonable number of realisations. Keywords: Safety assessment, sensitivity analysis, uncertainty analysis, PDF definition.

"ALUNPERIN VIALLISEN KAPSELIN" PERUSTAPAUKSEN TODENNÄKÖISYYSPOHJAISEN HERKKYYSTARKASTELUN TODENNÄKÖISYYSTIHEYKSIEN VALINTA

TIIVISTELMÄ

Posivan turvallisuusperustelun TURVA-2012 loppusijoitusjärjestelmän päästöskenaariot on tunnistettu raportissa Loppusijoituslaitoksen päästöskenaarioiden kuvaukset, POSIVA 2012-08. Tarkasteltavana on kolme kanisterin vikaantumismahdollisuutta ja siitä aiheutuvaa radionuklidien päästöä: (i) yhden kapselin alun perin kuparisen ulko-osan läpäisevä reikä, (ii) ulko-osan korroosio, joka tapahtuu nopeammin, jos puskurin tiheys on pienentynyt esimerkiksi eroosion johdosta, (iii) loppusijoitusreikää leikkaavan kallioraon siirros.

Mainitut kolme vikaantumismahdollisuutta on analysoitu deterministisesti raportissa Loppusijoituslaitoksen päästöskenaarioden tarkastelut, POSIVA 2012-09, ja toden-näköisyyspohjainen herkkyysanalyysi on suoritettu “alun perin viallisen kapselin perustapaukselle”.

Todennäköisyyspohjaisen herkkyysanalyysin päävaiheet olivat:

- mallin syöteparametrien epävarmuuden kvantifiointi todennäköisyystiheyksien avulla - järjestelmän kehityksen Monte Carlo -simulaatiot aina 106 vuoteen saakka käyttäen

edellä mainittuja todennäköisyystiheyksiä. Simulaatiot perustuivat 10 000 realisaatioon. - mallin tulosten epävarmuuden kvantifiointi, ja - niiden parametrien tunnistaminen, joiden epävarmuudella on suurin merkitys

mallinnustulosten kannalta (herkkyysanalyysi).

Tämä työraportti käsittelee todennäköisyyspohjaisen herkkyysanalyysin ensimmäistä vaihetta. Toisin sanoen se esittelee tarkasteltavat lähtötiedot ja todennäköisyystiheyksien muodostamisen menettelyn.

Rajoitetulle liukoisuudelle loppusijoituskapselin sisäosassa, ja jakautumiskertoimille puskurissa ja loppusijoitustunnelin täytteessä eri pohjavesikoostumuksilla on olemassa dataa (joilla katetaan geokemian epävarmuutta). Lisäksi epävarmuuden tekijät on kvantifioitu (formaali epävarmuus) kunkin vesikoostumuksen tapauksessa. Kaikkea tätä aineistoa on käytetty näiden parametrien lognormaalien jakaumien muodostamiseksi.

Lähi- ja kaukoalueen virtaukseen liittyvien parametrien todennäköisyystiheydet on luotu ajankohdan 5 000 AD hydrogeologisia reunaehtoja vastaavan pohjavesivirtausmallinnuksen perusteella.

Suurimmalle osalle muita parametreja käytetään logtasaisia todennäköisyystiheyksiä. Logtasaiset jakaumat liittävät saman todennäköisyyden kaikkiin suuruusluokkiin ja mahdollistavat syöteparametrien koko epävarmuusvälin otannan kohtuullisella realisaatioiden määrällä. Avainsanat: Turvallisuusperustelu, herkkyysanalyysi, epävarmuusanalyysi, toden-näköisyystiheyksien määritys

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TABLE OF CONTENTS

ABSTRACT TIIVISTELMÄ

1 INTRODUCTION .................................................................................................... 3

2 INVENTORY ........................................................................................................... 5

2.1 Radionuclide inventory .................................................................................. 5

2.2 Inventory of stable isotopes .......................................................................... 7

2.3 Instant Release Fractions (IRF) .................................................................. 10

2.3.1 Gap and grain boundary inventory and IRFs from the zirconium alloys and other metal parts............................................ 11

2.3.2 Crud inventory ................................................................................. 15

2.3.3 PDFs for the Instant Release Fractions .......................................... 17

3 FUEL DATA .......................................................................................................... 21

4 CANISTER DATA ................................................................................................. 23

4.1 General data ............................................................................................... 23

4.2 Solubility limits ............................................................................................. 25

4.2.1 Solubility input data ......................................................................... 25

4.2.2 Solubility limits in canister interior ................................................... 30

4.2.3 Solubility limits at other locations .................................................... 34

4.2.4 Solubility limits at the groundwater/buffer interface ......................... 35

4.2.5 Solubility limits in the buffer ............................................................ 37

4.2.6 Solubility limits in the backfill ........................................................... 38

4.2.7 Comments ....................................................................................... 40

5 BUFFER DATA ..................................................................................................... 41

5.1 Porosity accessible for anions and diffusion coefficients ............................ 41

5.2 Distribution coefficients ............................................................................... 43

5.2.1 Input data ........................................................................................ 44

5.2.2 PDFs for Kd´s in buffer.................................................................... 45

6 BACKFILL DATA .................................................................................................. 49

6.1 Diffusion coefficients and accessible porosity for anions ............................ 50

6.2 Longitudinal dispersion in the backfill .......................................................... 52

6.3 Distribution coefficients ............................................................................... 53

6.3.1 Input data ........................................................................................ 54

6.3.2 PDFs for Kd´s in backfill .................................................................. 55

7 NEAR-FIELD FLOWS AND LENGTH OF DISPOSAL TUNNEL .......................... 59

8 FLOW-RELATED GEOSPHERE PARAMETERS ................................................ 63

8.1 Parameters provided by ConnectFlow ........................................................ 64

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8.2 Longitudinal dispersion (Peclet number) ..................................................... 68

9 UNALTERED ROCK PROPERTIES ..................................................................... 69

9.1 Porosity and diffusion coefficients ............................................................... 70

9.2 Maximum penetration depth in the unaltered rock ...................................... 72

9.3 Distribution coefficients in the unaltered rock .............................................. 74

9.3.1 Input data ........................................................................................ 75

9.3.2 Definition of the PDFs ..................................................................... 78

10 GEOSPHERE-BIOSPHERE ACTIVITY CONSTRAINTS ..................................... 81

11 REFERENCES ..................................................................................................... 83

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1 INTRODUCTION

This working report describes the process followed to define the probability density functions (PDFs) assigned to the uncertain input parameters in the model used in the Probabilistic Sensitivity Analysis (PSA) of the “initial defect in the canister” reference model. The purpose of a PSA is to identify the parameters that control the model results of interest (usually peak doses or peak normalized releases to the environment). To achieve this goal including the correlation between different model input parameters is counterproductive. If two parameters A and B are correlated, and parameter A has a strong effect on the output variable of interest but parameter B has no effect, the PSA will find that parameter B has a significant effect on the output also. Then it would be necessary to distinguish the parameters that have a real effect on the model output from those that seem to be important due to correlation but in reality have no effect. This topic is discussed in Section 14.3 of [6]. For the solubility limits in the canister interior and the distribution coefficients in the buffer and the backfill, there are data available for different groundwater compositions (which accounts for the geochemical uncertainty) and the different sources of uncertainty for a given water composition have been quantified (formal uncertainty). All these data have been used to create Log-Normal distributions for these parameters. For most of the remaining parameters Log-Uniform PDFs are adopted, because the possible range of values typically spans one or more orders of magnitude and the amount of data available does not allow creating a more detailed distribution. Log-Uniform distributions assign the same probability to all the orders of magnitude covered by the range of values, and allow sampling the whole range of uncertainty of the input parameters with a reasonable number of realisations. Using Log-Uniform PDFs overestimates the probability of bounding cases (maximum IRF inventory, maximum fuel alteration rate, minimum sorption on granite,…) that have the highest consequences. In the following sections the process followed to select the PDFs of the different parameters is presented. The PDFs selected are shown in different tables in cells highlighted in yellow, to allow rapid identification. Significant work was dedicated to identify the uncertainty in the input parameter values and the PDFs have been selected to cover that uncertainty. It must be kept in mind that the conclusions of the PSA regarding the importance of the different uncertain parameters are valid only for the ranges of values explored. For this reason, wide ranges of values are usually selected for the uncertain parameters, so that the conclusions of the PSA will be valid for the many different calculation cases analysed in the Assessment of Radionuclide Release Scenarios [10].

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5

2 INVENTORY

Only Cl, I and Se are assumed to be in anionic form in the calculations. The remaining elements transport as cations or neutral species.

2.1 Radionuclide inventory

The radionuclide inventory used in the PSA has been taken from [15], where it is selected following a cautious approach: for each radionuclide the value selected is the maximum inventory in the different fuel elements to be disposed of in the repository. Data for radionuclides are shown in Table 2-1, where the inventory is in GBq/tU. In TURVA-2012 safety case each canister contains 2 tonnes of uranium. Half-lives in Table 2-1 have been taken from Table 6-5 of [10]. Figure 2-1 shows the decay chains considered in the calculations. Table 2-1. Radionuclide inventory used in the Reference Case of [10] and the PSA. Half-lives used in the PSA.

Radionuclide Half-life (a)

Inventory at 30 years cooling time (GBq/tU)

Fuel matrix Zirconium

alloys Other metal

parts Total

Ag-108m 4.38·102 4.08·10-3 0 2.50·104 2.50·104

Am-241 4.32·102 1.93·105 0 0 1.93·105

Am-243 7.37·103 3.42·103 0 0 3.42·103

Be-10 1.51·106 1.23·10-2 2.83·10-7 0 1.23·10-2

C-14 5.70·103 3.37·101 2.44·101 9.65·101 1.55·102

Cl-36 3.01·105 1.40 4.80·10-1 0 1.88

Cm-245 8.42·103 1.03·102 0 0 1.03·102

Cm-246 4.71·103 3.57·101 0 0 3.57·101

Cs-135 2.30·106 3.26E·101 0 0 3.26·101

Cs-137 3.01·101 3.48E·106 0 0 3.48·106

I-129 1.57·107 1.91 0 0 1.91

Mo-93 4.00·103 3.32·10-1 4.30·10-2 2.22·101 2.26·101

Nb-91 6.80·102 2.54·10-4 3.20·10-5 0 2.86·10-4

Nb-92 3.47·107 2.82·10-6 2.32·10-4 0 2.35·10-4

Nb-93m 1.61·101 8.33·101 4.99·103 0 5.07·103

Nb-94 2.03·104 1.81·10-2 3.22·102 4.30·102 7.52·102

Ni-59 7.60·104 7.32·10-1 6.27 2.14·102 2.21·102

Ni-63 1.01·102 8.63·101 8.15·102 2.38·104 2.47·104

Np-237 2.14·106 2.37·101 0 0 2.37·101

Pa-231 3.28·104 1.39·10-3 0 0 1.39·10-3

Pd-107 6.50·106 9.72 0 0 9.72

Pu-238 8.77·101 2.64·105 0 0 2.64·105

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Pu-239 2.41·104 1.42·104 0 0 1.42·104

Pu-240 6.56·103 2.92·104 0 0 2.92·104

Pu-241 1.43·101 1.75·106 0 0 1.75·106

Pu-242 3.75·105 2.08·102 0 0 2.08·102

Ra-226 1.60·103 0 0 0 0 Se-79 3.27·105 4.62 0 0 4.62

Sm-151 9.00·10 1.74·104 0 0 1.74·104

Sn-126 2.30·105 3.92·101 0 0 3.92·101

Sr-90 2.88·10 2.12·106 0 0 2.12·106

Tc-99 2.11·105 8.23·102 0 0 8.23·102

Th-229 7.34·103 0 0 0 0 Th-230 7.54·104 1.32·10-2 0 0 1.32·10-2

Th-232 1.40·1010 0 0 0 0 U-233 1.59·105 3.86·10-3 0 0 3.86·10-3

U-234 2.46·105 5.53·101 0 0 5.53·101

U-235 7.04·108 8.15·10-1 0 0 8.15·10-1

U-236 2.34·107 1.34·101 0 0 1.34·101

U-238 4.47·109 1.16·101 0 0 1.16·101

Zr-93 1.61·106 1.10·102 1.54·101 0 1.26·102

Figure 2-1. Decay chains considered in the PSA.

Cm-245

Pu-241

Am-241

Np-237

U-233

Th-229

Pu-240

U-236

Th-232

Am-243

Pu-239

U-235

Pa-231

Mo-93

Nb-93m

Cm-246

Pu-242

U-238

U-234

Th-230

Ra-226

Pu-238

Zr-93

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2.2 Inventory of stable isotopes

The total (stable and radioactive) inventory of the chemical elements present in the spent fuel has been taken from [15], which identifies both the maximum and the minimum element wise inventories in the different fuel elements to be disposed of in the repository. Table 2-2. Minimum and maximum elementary (stable + radioactive) inventory in the different spent fuel elements considered in TURVA-2012 safety case. (Shaded cells indicate elements for which the minimum and maximum differ by a factor > 3)

Element

Fuel matrix (mol/tU)

Zirconium-based alloys (mol/tU)

Other metal parts (mol/tU)

Minimum Maximum Minimum Maximum Minimum Maximum

Ag 8.13·10-1 1.44 0 0 2.06·102 2.06·102

Am 8.07 8.07 0 0 0 0 C 0 0 0 0 7.98* 1.39·101

Cl 0 0 1.52·10-1 3.48·10-1 0 0 Cm 3.07·10-2 4.31·10-1 0 0 0 0 Cs 1.92·101 2.82·101 0 0 0 0 I 1.87 3.00 0 0 0 0 Mo 4.22·101 6.31·101 0 0 1.22 1.98·101

Nb 1.39·10-4 2.14·10-4 9.40·10-2 6.51·101 4.95·10-3 3.43

Ni 0 0 0 0 1.21·102 3.49·102

Np 2.53 3.84 0 0 0 0 Pd 1.55·101 3.13·101 0 0 0 0 Pu 4.21·101 4.83·101 0 0 0 0 Ra 0 0 0 0 0 0 Se 8.09·10-1 1.20 0 0 0 0 Sm 6.83 9.68 0 0 0 0 Sn 4.96·10-1 8.47·10-1 4.24·101 5.60·101 0 0 Sr 8.06 1.16·101 0 0 0 0 Tc 9.56 1.37·101 0 0 1.87·10-2 4.99·10-2

Th 8.87·10-5 1.02·10-4 0 0 0 0 U 3.88·103 3.99·103 0 0 0 0 Zr 5.00·101 7.41·101 4.04·103 4.88·103 0 0

*Not used in the Reference Case of [10] because an unlimited solubility is assigned to carbon in that case. For most chemical elements, differences between the minimum and the maximum inventory in the different spent fuels are small. Light blue cells in Table 2-2 identify the three elements with a difference greater than a factor 3: curium, molybdenum and niobium.

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For fission products this is a logical result since inventory is roughly proportional to the fuel burnup, which can be expected to change a factor of 2 or 3 at most. The inventory of lighter actinides (such as Np) displays a similar linear dependence on burnup. The inventory of heavier actinides (such as Cm) in high burnup fuels is much higher than in low burnup fuels. Cm inventory is roughly proportional to burnup to the fourth power1, and a factor 2 of difference in burnup translates into a factor 16 of difference in the Cm inventory. Only for Nb in the zirconium alloys and Mo and Nb present in the “other metal parts” there are great differences between the minimum and the maximum amounts in the fuel. This is a consequence of the different compositions of the alloys present in the fuel elements used in the fuel from the Olkiluoto and Loviisa nuclear power plants. Reference Case in the Assessment of Radionuclide Release Scenarios For the Reference Case in the deterministic calculations [10] a conservative approach is followed and the minimum elementary amounts are used in the calculations, which allow less precipitation hence a higher concentration of radionuclides in solution. PSA For most elements the range of variation of the elemental inventory is small (less than a factor 3) compared with the many other uncertainties in the system, and it is not necessary to include this uncertainty in the model used in the PSA. For most elements the minimum elementary inventories are used, as in the Reference Case. Since there are no stable isotopes of Cm, the elemental inventory of Cm is not used in the calculations. Long lived Cm isotopes Cm-245 and Cm-246 are already included in the inventory (Table 2-1). Only for Nb in the zirconium alloys and Mo and Nb in other metal parts the elementary inventory presents an important variation between fuel elements. Mo-93 and Nb-94 in the zirconium alloys and other metals have been produced mostly by neutron activation of the Mo and Nb present in the alloys. The cautiously selected inventories of Mo-93 and Nb-94 in the zirconium alloys and other metals selected for the Reference Case have been used in the PSA. But these high values of Mo-93 and Nb-94 activities in the zirconium alloys and other metals are possible only if the fuel has a high content of Mo and Nb in their composition before irradiation. It is unrealistic to use high inventories of Mo-93 and Nb-94 with very low inventories of stable Mo and Nb in the zirconium alloys and other metals, and the results of the PSA could be unrealistic also. To avoid this problem, the PSA calculations are done using the highest elementary inventories of Nb in the zirconium alloys and other metal parts, and of Mo in other metal parts (light blue cells in Table 2-4).

1This empirical relationship is due to the production mode of Cm-244 by successive neutron captures.

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Finally, no inventory of stable Sn in the fuel matrix is considered in the PSA. The 3.92·1010 Bq/tU of Sn-126 (Table 2-1) correspond to 6.81·10-1 mol/tU, a value greater than the 4.96·10-1 mol/tU (minimum amount of total Sn in the fuel matrix in Table 2-2) and the inventory of stable Sn would be negative. This is a consequence of the cautious approaches followed for the inventory selection: while for radionuclides the maximum values (Bq/tU) are selected, for elements the minimum values (mol/tU) are adopted. Results in Table 2-3 clarify the effect of the inventory of stable niobium on the results of the PSA. Table 2-3 shows the Rank Correlation Coefficients (RCCs) for Nb-94 peak release rates from the near field and to the environment in the “hole forever” and “growing hole” cases defined in [6] considering stable niobium in the calculations (using the maximum amounts of niobium in Table 2-2) and without including stable niobium. Table 2-3. Rank Correlation Coefficients of Nb-94 peak release rates from the near field with and without stable Niobium.

Considering stable Niobium

Without stable Niobium

Hole forever

Hole forever

Hole forever

Growing hole

Canister failure Time to small hole creation Small hole diameter 0.341 0.361 De in the small hole 0.298 0.332 Time to loss of hole resistance -0.136 -0.124 Length of canister failed -0.038 -0.248 Waste IRF(Nb) in the crud Fuel alteration rate Zirconium alloys alteration rate -0.096 -0.044 Metals alteration rate Canister interior Cavity water volume Mass of buffer in cavity -0.075 -0.027 -0.349 -0.108 Solubility (Nb) 0.633 0.662 0.295 0.137 Hole Buffer De (cations/neutral) 0.238 0.381 0.253 0.437 Kd (Nb) -0.412 -0.421 -0.523 -0.551 Solubility correction factor (Nb) 0.133 0.044 Groundwater-buffer interface Solubility correction factor (Nb) Tunnel backfill De (cations/neutral) Kd (Nb) Solubility correction factor (Nb) Tunnel length Near field flows QF 0.183 0.215 0.201 0.285 QDZ 0.173 0.210 0.181 0.250 QTDF qTDZ R2 0.910 0.891 0.860 0.748 Threshold of significance 0.040 0.037 0.036 0.028

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If stable niobium is neglected, Solubility (Nb) inside the canister or in the buffer is identified as a far less important parameter than in the case in which stable niobium is considered, especially in the growing hole case. In addition, the importance of the Mass of buffer in cavity is overestimated if stable niobium is not included in the inventory. In order to obtain realistic results in the PSA, in the Monte Carlo simulations used for the PSA, the maximum values of niobium in the zirconium alloys and of molybdenum and niobium in the other metal parts in Table 2-2 have been adopted (Table 2-4). Table 2-4. Total (radioactive + stable isotopes) inventory of some chemical elements in the spent fuel used in the deterministic Reference Case [10] and the PSA.

Element Inventory after 30 years of cooling (mol/tU)

Fuel matrix Zirconium alloys Other metal parts

Ag 8.13·10-1 - 2.06·102

C - - 7.98

Mo 4.22·101 - 1.22 (RC)

1.98·101 (PSA)

Nb 1.39·10-4 9.40·10-2 (RC) 6.51·101 (PSA)

4.95·10-3 (RC)

3.43 (PSA) Ni - - 1.21·102

Pd 1.55·101 - -

Se 8.09·10-1 - -

Sn (*) 4.96·10-1 (RC)

- (PSA) 4.24·101 -

Sr 8.06 - -

Zr 5.00·101 4.04·103 -

(*) No inventory of stable Sn in the fuel matrix is considered in the PSA, as explained in the text.

Note that the data in Table 2-4 are the total masses (the sum of stable and radioactive isotopes) of the chemical elements after 30 years of cooling.

2.3 Instant Release Fractions (IRF)

The Instant Release Fraction (IRF) represents the fraction of the radionuclide inventory that is modelled to be released instantaneously to the interior of the canister, upon contact with water. While radionuclides immobilised in the UO2 matrix will be released gradually (at the conversion rate of the fuel matrix), the fraction of the radionuclides located at the fuel-clad gap and the grain boundaries will be released more rapidly. For the time scale of a safety assessment it is justified to consider this fast release as instantaneous. In addition to gap and grain boundary inventory, the inventory in the “crud” (a deposit of corrosion products on the outer surface of the cladding) is also included in the IRF, because the leaching properties of the crud in repository conditions are largely unknown. Finally, a fraction of the inventories of C-14 created by neutron

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capture of the nitrogen impurities in zirconium alloys and other metal parts, and Ag-108m from the Rod Control Cluster Assembly (RCCA) are also included in the IRF.

2.3.1 Gap and grain boundary inventory and IRFs from the zirconium alloys and other metal parts

Table F-2 of [10] summarises the IRFs for the reference inventory used in TURVA-2012 safety case. The values are shown in Table 2-5. The selection of the PDFs for the IRFs used in the PSA has been done mainly on the basis of Table 2-5, the report Werme et al. 2004 [3], the values used in the previous safety assessment RNT-2008 [9] and the values used in SKB TR-10-52 [4] (particularly the recommended values summarised in Table 2-6). Table 2-5. The Instant Release Fractions (IRF) chosen for the reference inventory (Table F-2 of [10]).

Element IRF of UO2

matrix IRF of zirconium

alloys IRF of other metal parts

Ag 5% - 100%

Am - - -

Be 5% - -

C 10% 20% -

Cl 10% - -

Cm - - -

Cs 5% - -

I 5% - -

Mo 5% - -

Nb - - -

Ni 5% - -

Np - - -

Pa - - -

Pd 1% - -

Pu - - -

Ra - - -

Se 0.4% - -

Sm - - -

Sn 0.01% - -

Sr 1% - -

Tc 1% - -

Th - - -

U - - -

Zr - - -

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Table 2-6. Recommended Instant Release Fractions (IRFs) in SKB TR-10-52 [4]

BWR fuel PWR fuel

Element (normal PDFs)

Μ σ μ σ

Cl-36 0.057 0.033 - 0.13 0.093 -

Cs-135 0.019 0.011 - 0.043 0.031 -

Cs-137 0.019 0.011 - 0.043 0.031 -

I-129 0.019 0.011 - 0.043 0.031 -

Se-79 0.0029 0.0027 - 0.0065 0.047 -

Element (triangular PDFs)

Lower limit

Best estimate

Upper limit-

Lower limit

Best estimate

Upper limit-

Ag-108m 0.45 0.47 0.49 1.0 1.0 1.0

C-14 0.085 0.086 0.086 0.11 0.11 0.11

Mo-93 0.014 0.016 0.018 5.1·10-5 5.5·10-5 5.8·10-5

Nb-93m 0.020 0.023 0.026 6.5·10-7 6.9·10-7 7.3·10-7

Nb.94 0.021 0.024 0.027 6.4·10-7 6.8·10-7 7.1·10-7

Ni-59 0.013 0.015 0.017 1.6·10-3 1.6·10-3 1.7·10-3

Ni-63 0.013 0.015 0.017 1.4·10-3 1.5·10-3 1.6·10-3

Pd-107 0 0.002 0.01 0 0.002 0.01

Sn-126 0 3.0·10-4 0.001 0 3.0·10-4 0.001

Sr-90 0 0.0025 0.01 0 0.0025 0.01

Tc-99 0 0.002 0.01 0 0.002 0.01

Zr-93 1.1·10-5 1.3·10-5 1.4·10-5 6.3·10-8 7.0·10-8 8.5·10-8

The data related to the main radionuclides are presented in the next paragraphs. The determination of the IRF in the gap and grain boundaries is based on either fission gas release (FGR) data or on leaching tests, and additional considerations due to uncertainties in the long-term releases. Carbon-14 Leaching data for C-14 are summarised in Werme et al. 2004 [3], where it is recommended to use a triangular distribution with an upper value of 10% and best estimate of 5% (based on Johnson & Tait 1997 [8]), and a lower value of 0.1% for the IRF of C-14 created in the UO2 matrix. This is also supported by Monte Carlo inventory and partitioning calculations carried out with the code Serpent (see Appendix C of the Models and Data report [15]) show that the fraction of C-14 in the IRF inventory of the fuel matrix is 2.24% and that in the cladding is 15.3%. In the current understanding, an additional fraction of C-14 is believed to be instantaneously released from the oxide part of the zirconium alloys. The IRF in the zirconium alloys oxide can be up to 20% (Johnson and McGinnes 2002 [16],

13

Yamaguchi et al. 1999 [18]) and this fraction seems to be leached out fairly rapidly, although this is based on very few experimental results. This assumption about the C-14 in the zirconium alloys is also shared by SKB in SR-Site on cautious grounds [4]. It can be shown (Figure 2-2) that, even if all the C-14 inventory in the zirconium alloys inventory were readily available (i.e. considered as IRF) this would have a marginal impact on the results of the reference case (although it may have some impact in some special what if scenario with releases earlier than 10,000y). This extreme case is included in the PSA for the initial defect in the canister reference model, via the use of a PDF for the IRF of carbon in the zirconium alloys that spans from 0.01 to 1.0 (Table 2-6). The PSA [6] has confirmed the very small effect on the model results of assuming very high values of the C-14 IRF in zirconium alloys.

Figure 2-2. Releases of C-14 from the canister taking into account its decay, the residence time in the canister (referred to “canister half-life,100 000 years) and different assumptions on the times of release of the entire inventory from the waste (from instant release to constant release along 10,000 years) reflecting the uncertainty in the release rates of C-14. The total inventory of C-14 in one canister has been assumed to be 40GBq.

Chlorine-36 There are few leaching data for Cl-36 release from light water reactor fuel, and hence estimates of the IRF done in Werme et al. 2004 [3] are based on CANDU fuel data. Data for CANDU fuel show that Cl-36 release increases steeply with fission gas release and it is three times the fission gas release for higher linear power ratings (LPRs). Although the LPR of light water reactor fuel is smaller than for CANDU fuel, Cl-36 IRF is assumed to be three times the FGR. In Werme et al. 2004 [3] a triangular distribution from 1% to 10%, with a most probable value of 5% is recommended.

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

0

0.5

1

1.5

2

2.5

3x 10

5 C-14 release periods

Time (a)

Rel

ease

(B

q/a)

Release from the canister with "half-life" 1e5 a

Instant1000 a2000 a5000 a1e4 a

14

In SKB TR-10-52 [4] the IRF for Cl-36 in the fuel matrix is determined assuming that it is three times the FGR (as in [3]). This assumption leads to relatively high mean values of the IRF for Cl-36: 5.7% for BWR fuel and 13% for PWR fuel (Table 2-6). Iodine-129 Werme et al. 2004 [3] present different experimental data related to the relationship between I-129 IRF and the FGR. I-129 gap release is much smaller than the FGR is some experiments, but the combined gap and grain boundary inventories seems to be approximately equal to the FGR. The recommended distribution for the IRF of I-129 is triangular from 0% to 2.5%, with a maximum at 1%. Measurements of the fractional release of I-129 from various high burn-up fuel rods (58 to 75 MWd/kgU) into aqueous solution over about 100 days have been performed (Johnsson et al. 2012 [21]). For I-129, the ratio of fractional release to FGR release appears to be of the order or slightly less than FGR. In SKB TR-10-52 [4] a 1:1 correlation between the IRF for I-129 and FGR is assumed, and the recommended mean value of the IRF for I-129 is 1.9% for BWR fuel and 4.3% for PWR fuel (Table 2-6). In the Reference Case [10] 5% of the I-129 inventory is assumed to be part of the IRF. Se-79 In SKB TR-10-52 [4] it is assumed that the IRF for Se-79 is 0.15 times the FGR. Recent leaching experiment data suggest that Se-79 may not be preferentially released from the fuel matrix at all since Se-79 cannot be detected in any of the leaching solutions or in the blank (Johnson et al. 2012, Wilson (1990a,b). The mean values of the IRF for Se-79 recommended in SKB TR-10-52 [4] (Table 2-6) are quite low: 0.29% for BWR fuel and 0.65% for PWR fuel. In Werme et al. 2004 [3] it is recommended to use a triangular distribution from 0% to 0.1% with a most probable value of 0.03%. In the Reference Case [10] only 0.4% of the Se-79 inventory is assumed to be part of the IRF. The current value is proposed to take into account the uncertainty in the long-term releases of Se-79 from the pores of difficult access in the UO2 matrix. Cs-135 and Cs-137 Measurements of the fractional release of Cs-137 from various high burn-up fuel rods (58 to 75 MWd/kgU) into aqueous solution over about 100 days have been performed by Johnsson et al. (2012) [21]. For Cs-137 release, when the data produced in this study are combined with previously published data (Werme et al. 2004 [3]; Johnson and McGinnes 2002 [16]) the ratio of fractional release to FGR is in the range of the previously reported 1:3 ratio. This can be attributed to the ratio of the diffusion coefficients of Cs/Xe in UO2 (about 0.33) as noted in Johnsson et al. (2012). The correlation assumed in TR-10-52 [4] is 1:1, the same as for I-129 (5%), and is therefore very pessimistic. In the Reference Case [10] 5% of the Cs-135 and Cs-137 of the total inventories are assumed to be in the IRF.

15

2.3.2 Crud inventory

Crud inventory data has been taken from Table C-8 of SKB TR-10-13 [13] that provides the inventory of crud for a BWR canister with 12 fuel elements (second column in Table 2-7). Table C-8 data were selected since they showed the highest crud inventories. Since each BWR fuel element contains 175 kg of uranium (Table 2-4 of [13]), there are 2.1 tonnes of initial uranium per canister. The crud inventory per tonne of uranium is divided by the total inventory in the spent fuel (last column in Table 2-1) to obtain the fraction of total inventory in the crud (third column in Table 2-7). Radionuclides whose crud inventory represents more than (or close to) 10-5 times the total inventory are shown in light blue cells. For actinides and Tc-99, the crud inventory represents 10-7 times the total inventory at most. In the reference case (UO2 alteration rate equal to 10-7 a-1) the crud inventory is smaller than the release from the UO2 in one year. In the probabilistic calculations for the PSA, the range of values of the UO2 alteration rate is 10-8 to 10-6 a-1, and the inventory released from the UO2 in 0.1 to 10 years would be greater than the inventory in the crud. Taking into account the slow transport of actinides and Tc-99, releases from the near field become significant only after thousands of years, and the activity released from the fuel up to that instant is nearly identical with and without crud. For this reason no IRFs of actinides from the crud are included in the model for the PSA.

16

Table 2-7. Crud inventory and fraction of the total inventory in the fuel in the crud. Radionuclides whose crud inventory represents more than (or close to) 10-5 times the total inventory are shown in light blue cells.

Radionuclide Crud inventory

(Bq/canister) [13] Fraction of total inventory in

the crud

Ag-108m 4.96·108 9.4·10-6

Am-241 3.12·107 7.7·10-8

Am-243 3.91·105 5.5·10-8

Cm-245 1.02·104 4.7·10-8

Cm-246 3.08·103 4.1·10-8

Mo-93 7.79·106 1.6·10-4

Nb-93m 4.59·1010 4.3·10-3

Nb-94 2.84·108 1.8·10-4

Ni-59 7.03·109 1.5·10-2

Ni-63 7.14·1011 1.4·10-2

Np-237 3.53·103 7.1·10-8

Pu-238 3.16·107 5.7·10-8

Pu-239 2.05·106 6.9·10-8

Pu-240 3.38·106 5.5·10-8

Pu-241 9.81·107 2.7·10-8

Pu-242 2.30·104 5.3·10-8

Tc-99 1.18·106 6.8·10-7

Th-230 3.94·100 1.4·10-7

U-234 1.07·104 9.2·10-8

U-235 8.81·101 5.1·10-8

U-236 2.18·103 7.8·10-8

U-238 1.98·103 8.1·10-8

Zr-93 3.15·106 1.2·10-5

For Ag-108m the crud inventory is 10-5 times the total inventory. Due to the lack of data on Rod Control Cluster Assembly (RCCA), the model takes this large uncertainty into account by using a Log-Uniform distribution between 0.05 and 1 (see section 2.3.3 ). A crud inventory in the order of 10-5 times the total inventory would have no effect compared with the IRF from the RCCA already included, which is 5000 times greater as a minimum. For this reason no IRF of Ag-108m due to crud has been included in the model. Table 2-7 shows that only Mo, Nb, Ni and Zr have a crud inventory that represents more than 10-5 times the total inventory. Only these 4 elements have an IRF due to crud in SKB TR-10-52 [4], and only for these 4 elements an IRF due to the crud inventory is included in the PSA.

17

2.3.3 PDFs for the Instant Release Fractions

The data in Sections 2.3.1 and 2.3.2 have been used to create the PDFs for the IRFs: - Ag in the fuel matrix: In the reference inventory (Table 2-5) the IRF of Ag in the

fuel matrix is 0.05. In page 79 of SKB TR-10-52 [4] it is stated that: “the contribution from the gap and grain boundary inventory (of Ag108m) is in the order of 1%”. An upper limit of 0.05 is adopted to include the value used in the reference scenario, and the lower limit is set ten times smaller. A Log-Uniform distribution is defined.

- Ag in the other metal parts: In the reference inventory (Table 2-5) an IRF equal to 1 is used. A constant IRF of 1 is recommended also in SKB TR-10-52 [4] (Table 2-6), because Ag inventory is mainly in the Ag-In-Cd of the RCCA and pessimistically it is assumed to be released instantaneously, due to the lack of data on silver release rate from the RCCA. A broad Log-Uniform distribution from 0.05 to 1 is adopted.

- Be: There are no readily available data for beryllium. The IRF of 0.05 used in reference inventory (Table 2-5) is adopted as the upper limit, and the lower limit is set ten times smaller. A Log-Uniform distribution is defined.

- C in the fuel matrix: An IRF of 0.10 is used in the reference inventory (Table 2-5). The ranges of recommended values for the IRF of the C-14 inventory in the fuel matrix given in SKB TR-10-52 [4] (Table 2-6) are very narrow: 0.085 to 0.11. Due to the scarce data available, a broad Log-Uniform distribution from 0.01 to 0.50 is adopted.

- C in zirconium alloys: For the C-14 inventory in the zirconium-based alloys the current understanding is that 20% of the C-14 of the cladding is in the oxide layer of the zirconium-based alloys. However, this is based on very few experimental results. This value of 0.20 is used in the reference inventory (Table 2-5). Due to the limited data available and the uncertainty on the thickness of the oxidized layer, a very broad Log-Uniform distribution from 0.01 to 1 is adopted.

- C in the other metal parts: Due to the total lack of data on C-14 release from the other metal parts a very broad Log-Uniform distribution from 0.01 to 1 is adopted.

- Cl: In the reference inventory (Table 2-5) the IRF represents 10% of the Cl inventory in the fuel matrix. In SKB TR-10-52 [4] (Table 2-6) normal distributions are recommended for Cl-36 IRF, with μ=0.057 and σ=0.033 for the BWR fuel, and μ=0.13 and σ=0.093 for the PWR fuel. Since values in SKB TR-10-52 [4] are based on fission gas release fractions, it is clear that they represent the IRF of the Cl-36 inventory in the UO2 matrix (not the total inventory). An upper limit of 0.20 is selected for IRF(Cl) in the fuel matrix, which corresponds roughly to μ+σ for the PWR fuel. The lower limit is set ten times smaller: 0.02. Since the range spans one order of magnitude, a Log-Uniform distribution is selected.

- Cs: The IRF(Cs) in the reference inventory (Table 2-5) is 0.05, the same fraction as in RNT-2008 [9]. In SKB TR-10-52 [4] (Table 2-6) normal distributions are recommended for cesium IRF, with μ=0.025 and σ=0.021 for BWR fuel, and μ=0.43 and σ=0.031 for the PWR fuel. The upper limit is set on the basis of μ+2σ for the PWR type canister, rounded to 0.10. The lower limit is set ten times smaller: 0.01.

18

Since the range spans one order of magnitude, a Log-Uniform distribution is selected.

- I: The IRF(I) in the reference inventory (Table 2-5) is 0.05. In SKB TR-10-52 [4] (Table 2-6) normal distributions are recommended for iodine IRF, with μ=0.025 and σ=0.021 for BWR fuel, and μ=0.43 and σ=0.031 for the PWR fuel, leading to μ+2σ=0.105 at most. The upper limit is set equal to 0.15 in order to explore the potential effect of high burnup PWR fuel (such as OL3), for which FGRs of up to 0.15 have been obtained [19]. The lower limit is set ten times smaller: 0.015. Since the range of values spans over one order of magnitude, a Log-Uniform distribution is selected.

- Mo: In the reference inventory (Table 2-5) 5% of the Mo inventory in the fuel matrix is in the IRF, while the zirconium alloys and other metals have no IRF. In SKB TR-10-52 [4] it is considered that “the only source of the IRF of Mo is the crud inventory”, and the recommended values for the IRF of Mo inventory in zirconium alloys and other metals (Table 2-6) are very low (in the order of 5·10-5) for PWR fuel and much higher values (0.014 to 0.018) for BWR fuel. For the PSA both the IRF of Mo in the fuel matrix and due to the crud will be included, in order to identify their possible influence. For the IRF of Mo in the fuel matrix the value of 0.05 used in the reference inventory is adopted as upper limit of the PDF and the lower limit is set 10 times smaller. A Log-Uniform distribution is adopted. For the IRF of Mo in the zirconium alloys and other metals (that represents the crud inventory) an upper value of 0.02 is adopted on the basis of the upper limit in SKB TR-10-52 [4] (Table 2-6), and the lower limit is 10 times smaller. A Log-Uniform distribution is adopted.

- Nb: In the reference inventory (Table 2-5) the IRF of Nb is zero. In SKB TR-10-52 it is considered that “the only source of the IRF of Nb is the crud inventory” and the recommended values for the IRF of Nb inventory in zirconium alloys and other metals are low (Table 2-6): between 5·10-7 and 0.027 for PWR fuel and between 0.020 and 0.027 for BWR fuel. For the PSA no IRF of Nb in the fuel matrix is considered, but an IRF of the Nb inventory in the zirconium alloys and other metals (associated to the crud) is included in order to identify its possible influence. A Log-Uniform PDF is adopted for this parameter, with the upper limit equal to 0.03 and the lower limit 10 times smaller.

- Ni: In the reference inventory (Table 2-5) the IRF of Ni in the fuel matrix is 0.05, while there is no IRF in the zirconium alloys and the other metals. In SKB TR-10-52 [4] it is considered that “the only source of the IRF of Ni is the crud inventory”, and the recommended values for the IRF of Ni inventory in the zirconium alloys and other metals are low (Table 2-6): between 10-3 and 0.017 for PWR fuels and between 0.013 and 0.017 for BWR fuels. For the PSA both the IRF of Ni in the fuel matrix and due to the crud are considered. For the IRF of Ni in the fuel matrix the value of 0.05 used in the reference scenario is adopted as upper limit of the PDF and the lower limit is 10 times smaller. A Log-Uniform distribution is adopted. For the IRF of Ni in the zirconium alloys and other metals (that represents the crud inventory) an upper limit of 0.02 is selected on the basis of the upper limit in SKB

19

TR-10-52 [4] and data in Table 2-7 (around 0.015), and the lower limit is 10 times smaller. A Log-Uniform distribution is adopted.

- Pd, Sr and Tc: The IRF of the three elements in the reference inventory (Table 2-5) is 0.01. This is the upper limit of the recommended values in SKB TR-10-52 [4] (Table 2-6), where best estimates are around 0.002 and lower limits are zero. The range of values adopted is 0.001 to 0.01 covering one order of magnitude, and a Log Uniform distribution is used.

- Se: In SKB TR-10-52 [4] (Table 2-6) normal distributions are recommended for Se-79 IRF, with μ=0.0065 and σ=0.0047 for the PWR fuel (μ+2σ=0.0159), with smaller values for the BWR fuel. An upper limit of 0.02 is selected, with a lower limit ten times smaller: 0.002. This range of values includes the value of 0.004 adopted for the reference inventory (Table 2-5), and since the range spans one order of magnitude a Log Uniform distribution is selected.

- Sn: A value of 0.0001 is used in the reference inventory (Table 2-5). In SKB TR-10-52 [4] (Table 2-6) the upper limits are 0.001, best estimates are 3·10-4 and lower limits are zero both for BWR and PWR fuels. The range of values adopted is 0.0001 to 0.01, spanning from the value in the reference inventory to ten times the upper limit in SKB TR-10-52 [4]. A Log Uniform distribution is used.

- Zr: No IRF of zirconium is used in the reference inventory (Table 2-5). In SKB TR-10-52 [4] it is considered that “the only source of the IRF of Zr is the crud inventory”, and very low values are recommended for the IRF of Zr inventory in the zirconium alloys and other metals (Table 2-6): between 6·10-8 and 10-5 for PWR fuel and in the order of 10-5 for BWR fuel. For the PSA no IRF of Zr in the fuel matrix is considered, but an IRF of the Zr inventory in the zirconium alloys and other metals (associated to the crud) is included. The upper limit of the recommended values in SKB TR-10-52 [4] (Table 2-6) is very small (10-5 times the total Zr-93 inventory, that corresponds to roughly 10-4 times the Zr-93 inventory in the zirconium alloys) and similar to data in Table 2-7. In order to identify any possible effects, Log-Uniform distribution from 10-4 to 10-2 (of Zr inventory in the zirconium alloys) is adopted. It must be kept in mind that the activity in the crud is calculated as the product of the IRF in the crud times the radionuclide inventory in the zirconium alloys (not in the complete fuel element).

20

Table 2-8. Instant Release Fractions. Values used in the Reference Case [10] and PDFs for the PSA. LU= log-uniform distribution.

Element Value in the

Reference Case PDF for the PSA

IRF of the inventory in the fuel matrix

Ag 0.05 LU (0.005 – 0.05)

Be 0.05 LU (0.005 – 0.05)

C 0.10 LU (0.01 – 0.50)

Cl 0.10 LU (0.02 – 0.20)

Cs 0.05 LU (0.01 – 0.10)

I 0.05 LU (0.015 – 0.15)

Mo 0.05 LU (0.005 – 0.05)

Ni 0.05 LU (0.005 – 0.05)

Pd 0.01 LU (0.001 – 0.01)

Se 0.004 LU (0.002 – 0.02)

Sn 0.0001 LU (0.0001 – 0.01)

Sr 0.01 LU (0.001 – 0.01)

Tc 0.01 LU (0.001 – 0.01)

IRF of the inventory in the zirconium alloys

C 0.20 LU (0.01 – 1.0)

IRF of the inventory in the other metal parts

Ag 1 LU (0.05 –1)

C 0 LU (0.01 – 1.0)

IRF due to the crud (IRF of the inventory in the zirconium alloys and other metal parts)

Mo 0 LU(0.002 – 0.02)

Nb 0 LU(0.003 – 0.03)

Ni 0 LU(0.002 – 0.02)

Zr 0 LU (0.0001 – 0.01)

The inventory in the crud is not considered in the Reference Case of [10] safety case, due to lack of published data on Loviisa and Olkiluoto fuel (however it has been taken into account in a complementary case). In the PSA [6] the inventory in the crud is taken into account assigning the PDFs in Table 2-8 to the IRFs of Mo, Nb, Ni and Zr inventories in the zirconium alloys and other metals. These are the 4 elements identified in Table 2-7 and in SKB TR-10-52 [4] as having a significant inventory in the crud. The same IRFs are applied to all the isotopes (radioactive and stable) of a given chemical element.

21

3 FUEL DATA

The PDFs for the dissolution or corrosion rates of the three separate components of the spent fuel considered (UO2 matrix, zirconium alloys and other metal parts) have been created dividing and multiplying by 10 the values used in the Reference Case, to obtain the minimum and the maximum value, respectively. Log-Uniform distributions from the minimum to the maximum values are adopted for the three dissolution/corrosion rates. Fuel parameter values used in the Reference Case and PDFs adopted for the PSA are summarised in Table 3-1. Table 3-1. Fuel data. Values used in the Reference Case and PDFs for the PSA. LU= Log-uniform distribution

Parameter Value in the


Mass of U per canister (tU) 2 Constant (2)

Fuel matrix fractional dissolution rate (a-1) 10-7 LU (10-8 – 10-6)

Zirconium alloys fractional dissolution rate (a-1) 10-4 LU (10-5 – 10-3)

Fractional corrosion rate for other metal parts (a-1) 10-3 LU (10-4 – 10-2)

22

23

4 CANISTER DATA

4.1 General data

In the “initial defect in the canister” reference model it is assumed that a disposal canister presents a manufacture defect in the copper overpack that, after some time, leads to establishment of a transport path from the canister interior to the bentonite buffer. This defect in the copper overpack is a small hole with a diameter in the order of 1mm (and a surface around 10-6 m2). In the Reference Case of [10] this small hole remains unchanged during all the calculation period (106 years), but additional calculation cases are included in which the initial small hole, after a given time period, becomes a much greater defect (in the order of 1 m2) leading to complete loss of the canister transport resistance. The Probabilistic Sensitivity Analysis (PSA) intends to provide useful information both for the calculations cases in which the initial small hole remains unchanged during all the calculation period (106 years) and the calculation cases in which the initial small hole grows into a much greater defect. After some testing, it has been found that, in order to obtain clear conclusions from the PSA, both cases must be treated separately: - two Monte Carlo simulations up to 106 years are performed, in one simulation the

small hole initially formed remains unchanged during all the calculation period in all the realisations and in the other simulation the small hole grows into a much greater defect after thousands or a few tens of thousands years, in all the realisations,

- the different sensitivity measures are calculated for both cases, and - the results are presented together in order to facilitate comparison (important

parameters if the small hole grows vs. important parameters if the small hole remains unchanged).

The delay time since the disposal of the defective canister in the deposition hole until the establishment of a transport pathway from the canister interior to the buffer is a highly uncertain parameter. In the Reference Case a delay time of 1,000 years is used, which rules out any possible consequences due to two fission products with large inventories: Cs-137 and Sr-90. Both radionuclides have half-lives around 30 years, and their inventories after 1,000 years are 10 orders of magnitude smaller than at the time of emplacement. Due to the great uncertainties in the value of this delay time, for the PSA a broad Log-Uniform distribution from 10 to 5,000 years is adopted. The lower limit of 10 years is roughly equivalent to the instantaneous formation of the transport path and the upper limit of 5,000 years is obtained multiplying by 5 the delay time in the Reference Case. The cavity water volume is also a highly uncertain parameter, due to the possible intrusion of bentonite into the canister interior and the build-up of corrosion products of the iron in the canister (that have a greater molar volume than the original iron). In addition, the identification of any influence is easier if a wider range of variation is adopted. For these reasons a Log-Uniform distribution is proposed, that spans one order of magnitude: 90 to 900 litres.

24

Table 4-1. Canister parameters. Values used in the Reference Case and PDFs for the PSA- LU=log-uniform distribution

Parameter Value in the


Number of failed canisters 1 Constant (1)

Location of the failed canister Location 381 of ps_r0_5000.csv

All the possible locations in ps_r0_5000.csv are sampled

Delay until establishment of transport path in canister interior (a) 1000 LU (10 - 5·103)

Cavity water volume (litres) 700 LU (90 - 900)

Mass of bentonite in the cavity (kg) 0 LU (1 - 103)

Diameter of the small hole (mm) 1 LU (0.3 – 3)

Diffusion coefficient within the small hole (m2/s) 10-9 LU (2·10-11 - 10-9)

Parameters related with the growth of the small hole

Delay between establishment of transport path in canister interior and loss of transport resistance of defect (a)

Not used (the small hole does

not grow) LU (5·103 - 5·104)

Size of the grown hole – Length of canister lateral surface failed (m)

Not used (the small hole does

not grow) LU (0.1 – 4.8)

Intrusion of bentonite into the canister cavity can be expected, both through the initial small hole in the canister and through the enlarged hole. The mass of bentonite (solid) that penetrates into the canister cavity is a very uncertain parameter, and for this reason a wide Log-Uniform distribution from 1 to 1000 kg is used. The lower limit corresponds to a very small mass of bentonite in the cavity (similar to the Reference Case, in which no bentonite intrusion is considered) while the high value is an extreme case in which most of the canister cavity is filled with bentonite. In the calculations it is assumed that the bentonite enters the cavity immediately after the formation of the transport path through the canister. No anion exclusion is considered in the water inside the canister, and anions (Cl, I and Se) can dissolve in the total volume of water in the canister cavity. No reduction of the density of the buffer in the deposition hole due to the bentonite intrusion into the cavity is considered in the calculations. Since the mass of bentonite (solid) in a deposition hole is 22,980 kg, the intrusion of 1,000 kg of bentonite into the cavity would produce only a 4.3% reduction of the buffer dry density: from 1.57 to 1.50 g/cm3, and hence the effects on the diffusion and sorption properties of the buffer are expected to be very small. The small hole in the copper overpack has a diameter of 1mm in the Reference Case. For the PSA a range of values to be used in the PSA is created multiplying and dividing this value by 3. A Log-Uniform distribution between 0.3 and 3mm has been adopted. The resulting value of the surface of the small hole spans two orders of magnitude: from 7.1·10-8 to 7.1·10-6 m2.

25

In the calculations in which the small hole grows, it is assumed that a much greater ring shaped defect is created in the uppermost lateral surface of the canister. The parameter used to quantify the size of the great hole is the “length of canister lateral surface damaged”. This parameter is represented using a Log-Uniform distribution between 0.1m and 4.8m (total length of the canister). The resulting damaged surface of the canister ranges from 0.33 to 15.8 m2. The calculation model used in the Probabilistic Sensitivity Analysis is based on the geometry of the deposition hole and tunnel for OL1&2 BWR fuel. The length of the deposition canister for OL1&2 is 4.8m. The canisters for other spent fuels to be disposed of in Olkiluoto have different lengths: 3.6m for LO1&2 and 5.25m for OL3 (the same assumed for OL4).

4.2 Solubility limits

4.2.1 Solubility input data

The input data related to solubilities have been taken from sections 4.1 to 4.5 of reference [11] and section 3 of reference [12]. References [11] and [12] provide, for each chemical element, reference solubilities for six different groundwaters and an upper limit for the solubility at four different locations in the near field: - inside the canister, - at the groundwater/buffer interface, - in the buffer porewater and - in the backfill porewater. When the references provide several sets of solubilities for a given element and location, those calculated using Andra database are selected [22]. For radium, solubilities derived for the reference waters based on solid solution formation are selected, because “coprecipitation and solid solution formation of (Rax,Ba1-x)SO4 is well established, and the Ba inventory in the waste is large” [11]. Table 4-2 to Table 4-5 present the input data used for the definition of the PDFs for the solubility limits used in the PSA. Solubility limits greater than 2.0·10-3 mol/l are shown as unlimited (unlim.) in the tables.

26

Table 4-2. Input data for the solubility limits inside the canister (taken from [11]).

Reference solubility value (mol/l) Upper limit

Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 9.9E-06 5.1E-06 6.9E-07 2.5E-04 1.0E-05 1.6E-06 2.5E-04

Am III 1.7E-06 6.0E-06 1.9E-06 2.7E-05 1.2E-08 3.3E-08 2.7E-05

Be II 1.4E-06 4.4E-06 2.2E-06 1.7E-06 1.7E-06 7.6E-07 4.4E-06

Cinorg 5.2E-04 1.1E-03 unlim. 2.4E-05 9.3E-06 2.5E-04 unlim.

Corg unlim. unlim. unlim. unlim. unlim. unlim. unlim.

Cl unlim. unlim. unlim. unlim. unlim. unlim. unlim.

Cm III 1.7E-06 6.0E-06 1.9E-06 2.7E-05 1.2E-08 3.3E-08 2.7E-05

Cs unlim. unlim. unlim. unlim. unlim. unlim. unlim.

I unlim. unlim. unlim. unlim. unlim. unlim. unlim.

Mo VI 3.1E-06 2.4E-06 1.6E-07 1.1E-10 4.2E-06 1.0E-04 unlim.

Nb V 9.5E-07 1.9E-07 3.4E-07 5.2E-07 unlim. 1.3E-04 unlim.

Ni II 9.3E-05 8.3E-04 1.2E-04 6.2E-05 1.2E-07 1.4E-07 8.3E-04

Np IV 1.0E-09 1.0E-09 1.2E-09 6.8E-10 9.5E-10 1.0E-09 1.3E-08

Pa V 1.0E-08 1.0E-08 1.3E-09 8.4E-10 6.1E-09 2.4E-09 1.0E-06

Pd II 3.7E-06 3.9E-06 4.0E-06 6.3E-06 3.8E-06 4.0E-06 1.2E-05

Pu III 1.2E-10 4.3E-10 1.8E-09 1.2E-09 1.3E-11 1.4E-11 3.0E-08

Ra II 1.6E-11 6.7E-11 7.2E-11 2.5E-08 1.8E-09 4.2E-10 8.7E-05

Se -II 5.8E-10 5.9E-11 3.3E-10 8.2E-09 2.0E-07 5.9E-09 3.4E-07

Sm III 6.1E-08 3.6E-07 1.3E-07 2.4E-06 6.8E-07 6.1E-09 1.2E-05

Sn IV 1.1E-07 6.3E-08 7.6E-08 7.0E-08 1.3E-05 4.2E-06 1.3E-05

Sr II 1.3E-04 7.4E-04 1.8E-04 unlim. unlim. 2.0E-05 unlim.

Tc IV 3.7E-09 3.9E-09 4.0E-09 2.8E-09 4.6E-09 4.2E-09 1.5E-08

Th IV 2.7E-09 4.2E-09 1.3E-08 1.1E-09 1.5E-09 2.1E-09 8.8E-07

U IV 4.1E-09 2.4E-08 9.4E-09 2.1E-09 3.0E-09 8.7E-09 3.0E-07

Zr IV 1.7E-08 1.8E-08 1.8E-08 1.2E-08 1.7E-08 1.8E-08 9.2E-07

27

Table 4-3. Input data for the solubility limits at the groundwater/buffer interface (taken from [11]).


Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 1.0E-05 5.2E-06 6.9E-07 2.5E-04 1.0E-05 1.6E-06 2.5E-04

Am III 1.1E-05 5.2E-06 2.3E-06 6.8E-05 1.2E-08 2.3E-08 6.8E-05

Be II 6.3E-06 7.1E-06 3.0E-06 7.4E-06 1.7E-06 9.3E-07 7.4E-06




Cm III 1.1E-05 5.2E-06 2.3E-06 6.8E-05 1.2E-08 2.3E-08 6.8E-05





Ni II 1.5E-03 2.1E-03 2.3E-04 1.4E-03 1.2E-07 1.2E-07 unlim.

Np IV 9.6E-10 1.0E-09 1.3E-09 7.0E-10 9.5E-10 1.0E-09 1.3E-08

Pa V 1.0E-08 1.0E-08 1.4E-09 1.4E-09 3.0E-09 1.0E-08 1.0E-06

Pd II 3.9E-06 3.9E-06 4.0E-06 8.5E-05 3.8E-06 4.0E-06 8.5E-05

Pu III 7.4E-09 1.1E-08 5.8E-09 3.4E-08 1.3E-11 1.4E-11 4.5E-07

Ra II 1.7E-09 6.7E-11 7.7E-11 2.4E-08 1.7E-09 4.1E-10 8.6E-05

Se -II 1.7E-09 4.9E-10 4.7E-10 1.2E-08 5.9E-09 1.3E-08 1.0E-06

Sm III 6.4E-07 5.3E-07 1.8E-07 4.2E-06 6.8E-07 5.4E-09 2.1E-05

Sn IV 5.9E-08 5.7E-08 6.9E-08 3.9E-08 1.3E-05 3.3E-06 1.3E-05

Sr II 5.0E-03 8.7E-04 1.8E-04 unlim. unlim. 2.7E-05 unlim.

Tc IV 3.8E-09 3.9E-09 4.0E-09 2.7E-09 4.6E-09 4.6E-09 1.5E-08

Th IV 3.3E-09 6.3E-09 2.0E-08 1.2E-09 1.5E-09 1.9E-09 1.2E-06

U IV 3.3E-09 6.3E-09 2.0E-08 1.2E-09 1.5E-09 1.9E-09 6.0E-08

Zr IV 1.7E-08 1.8E-08 1.8E-08 1.2E-08 1.7E-08 1.8E-08 9.2E-07

28

Table 4-4. Input data for the solubility limits in the buffer porewater (taken from [11]).


Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 3.0E-05 1.4E-05 1.0E-06 3.3E-04 1.0E-05 9.9E-07 3.3E-04

Am III 4.9E-07 6.3E-06 1.1E-06 9.2E-06 1.1E-08 3.3E-08 9.2E-06

Be II 1.9E-06 6.0E-06 1.9E-06 1.9E-06 1.9E-06 1.9E-06 6.0E-06




Cm III 4.9E-07 6.3E-06 1.1E-06 9.2E-06 1.1E-08 3.3E-08 9.2E-06





Ni II 1.9E-04 1.5E-03 1.0E-04 4.4E-04 1.2E-07 1.3E-07 1.5E-03

Np IV 9.1E-10 1.0E-09 1.2E-09 5.5E-10 9.5E-10 1.0E-09 2.1E-08

Pa V 1.0E-08 1.0E-08 1.3E-09 8.5E-10 6.2E-09 2.7E-09 1.0E-06

Pd II 3.4E-06 3.9E-06 4.0E-06 1.5E-04 3.8E-06 4.0E-06 1.5E-04

Pu III 8.4E-10 5.7E-09 2.4E-09 4.9E-09 1.3E-11 1.4E-11 9.9E-08

Ra II 1.4E-11 4.8E-11 5.1E-11 2.8E-08 1.7E-09 2.4E-10 unlim.

Se -II 1.4E-09 4.3E-10 4.5E-10 1.5E-08 5.8E-09 4.9E-09 8.1E-07

Sm III 1.7E-07 6.3E-07 1.3E-07 8.6E-07 2.4E-06 5.8E-09 2.1E-05

Sn IV 8.4E-08 5.9E-08 8.1E-08 3.4E-08 1.2E-05 2.8E-06 1.2E-05

Sr II 1.0E-03 6.7E-04 5.1E-04 unlim. 3.2E-04 1.6E-05 unlim.

Tc IV 3.4E-09 3.8E-09 4.0E-09 2.2E-09 4.6E-09 4.4E-09 1.4E-08

Th IV 3.6E-09 3.6E-09 1.6E-08 9.3E-10 1.5E-09 2.1E-09 7.5E-08

U IV 3.5E-09 3.7E-09 1.2E-08 1.7E-09 3.0E-09 6.9E-10 1.5E-07

Zr IV 1.5E-08 1.7E-08 1.8E-08 9.8E-09 1.7E-08 1.8E-08 9.2E-07

29

Table 4-5. Input data for the solubility limits in the backfill porewater (taken from [12]).


Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 2.8E-05 1.0E-05 1.1E-06 3.0E-04 2.8E-05 1.7E-06 3.0E-04

Am III 1.0E-05 1.1E-05 8.4E-06 3.9E-05 1.2E-08 7.0E-07 3.9E-05

Be II 2.5E-06 5.7E-06 4.9E-06 3.9E-06 1.8E-06 6.1E-07 5.7E-06

Cinorg 3.6E-04 8.6E-04 1.7E-03 8.1E-05 1.4E-05 4.4E-05 1.7E-03



Cm III 1.0E-05 1.1E-05 8.4E-06 3.9E-05 1.2E-08 7.0E-07 3.9E-05





Ni II 3.1E-04 1.7E-03 1.3E-03 3.5E-04 1.2E-07 1.4E-06 1.7E-03

Np IV 9.5E-10 1.0E-09 1.1E-09 6.1E-10 9.2E-10 9.9E-10 1.4E-08

Pa V 1.0E-08 1.0E-08 1.7E-09 8.6E-10 6.3E-09 1.3E-09 1.0E-06

Pd II 3.7E-06 3.8E-06 3.9E-06 8.4E-05 3.7E-06 3.9E-06 8.4E-05

Pu III 7.8E-10 6.3E-09 7.5E-09 3.5E-09 1.3E-11 1.4E-11 9.9E-08

Ra II 3.2E-11 3.2E-11 1.6E-11 1.0E-08 3.4E-11 1.7E-11 3.6E-05

Se -II 4.2E-10 2.8E-10 3.5E-10 5.1E-09 8.5E-10 4.3E-10 2.9E-06

Sm III 4.3E-07 7.2E-07 4.1E-07 2.2E-06 6.5E-07 8.5E-08 1.1E-05

Sn IV 7.4E-08 5.8E-08 6.2E-08 3.6E-08 1.4E-05 4.3E-07 1.4E-05

Sr II 3.7E-04 3.5E-04 1.3E-04 unlim. 3.8E-04 1.4E-04 unlim.

Tc IV 3.7E-09 3.8E-09 3.9E-09 2.3E-09 4.6E-09 4.0E-09 1.2E-08

Th IV 2.2E-09 3.5E-09 6.4E-09 9.2E-10 1.5E-09 1.7E-09 3.0E-08

U IV 3.1E-09 3.8E-09 5.6E-09 1.8E-09 2.9E-09 3.1E-09 3.5E-07

Zr IV 1.7E-08 1.7E-08 1.8E-08 1.0E-08 1.7E-08 1.8E-08 9.2E-07

30

4.2.2 Solubility limits in canister interior

In this section the PDFs for the solubilities inside the canister are obtained. Sections 4.2.4 to 4.2.6 describe the treatment in the PSA of the solubilities at the three other locations in the near field: - at the groundwater/buffer interface, - in the buffer porewater and - in the backfill porewater. Section 4.2.1 shows that Corg, Cl, Cs and I solubilities are unlimited (>2.0·10-3 mol/l) both inside the canister and in the rest of the near field for the six water compositions considered. As a consequence, in the PSA unlimited solubilities are assigned to Corg, Cl, Cs and I for the PSA. In order to represent the uncertainty in the solubilities in the canister interior, log-normal PDFs have been generated. Since solubility data typically span several orders of magnitude, a logarithmic distribution has been adopted to give similar weight to the different orders of magnitude covered by the PDF. Due to the significant amount of data available it has been tried to create realistic probability density function, with regions of values with a higher probability and other less likely values. The next paragraphs present the method followed to derive log-normal PDFs for the solubilities in the canister interior. The resulting distributions are summarised in Table 4-6 and represented in Figure 4-1. Definition of the log-normal PDFs Table 4-2 provides the following information for each chemical element: - The reference solubility value for 6 groundwaters (V1, V2, V3, V4, V5, V6) - The upper limit of the solubility (Upper limit) For some elements and water compositions the reference solubility value is “unlim”, which means that it is greater than 2·10-3 mol/l. In the selection of the PDFs the value 10-2 mol/l is used when the input data states that solubility is “unlimited”.

For each element, Maximum is defined as the highest value of V1, V2, V3, V4, V5 and V6 and Minimum is defined as the lowest value of V1, V2, V3, V4, V5 and V6. The range of values of the reference solubility values for the 6 groundwaters (Minimum to Maximum) covers the geochemical uncertainty of the parameter. In addition, the value of the solubility for a given groundwater composition is affected by some uncertainty in the thermodynamic data used to calculate the solubilities. This uncertainty is quantified using an element specific uncertainty factor. To simplify the generation of the PDFs for the solubilities, a thermodynamic uncertainty factor of 3 has been adopted for all the elements, and the “range of most probable values” spans from Minimum/3 to 3·Maximum.

31

When creating the PDFs for the solubilities it is intended to give a much higher weight in the distribution to the region of most probable values [Minimum/3, 3·Maximum], with the values outside that range being far less probable. Since solubilities typically span oven several orders of magnitude, log-normal distributions have been adopted, and defined in such a way that: - 90% of the cumulative distribution function (CDF), as a minimum, corresponds to

the “most probable values”, - 5% of the CDF, as a maximum, is smaller than Minimum/3, and - 5% of the CDF, as a maximum, is greater than 3·Maximum.

The mean of the log10 of the solubility is defined as the central value (in logarithms) of the range of the reference solubility values in the 6 groundwaters:

12

The standard deviation of the log10 of the solubility is defined in such a way that 90% of the probability corresponds to the region of most probable values

3 /3

2 ∗ 1.845, 0.27

To ensure that the “range of most probable values” used in the calculations covers at least one order of magnitude a minimum value of 0.27 for SD log10(Solubility) is imposed in the previous definition. Data in section 4.2.1 includes upper limits for the solubilities but does not provide lower limits. For each element the Lower limit is defined as 1/10th of the corresponding value of Minimum. Log-normal PDFs are truncated to avoid sampling values beyond these upper and lower limits:

/10

Note for carbon: Table 4-2 provides solubilities for organic carbon in the canister interior (unlimited for the 6 groundwaters) and for inorganic carbon in the canister interior. - For the solubility of inorganic carbon a log-normal distribution is created using the

solubilities of inorganic carbon in the 6 groundwaters, as explained in the previous paragraphs.

- For the solubility of organic carbon a log-uniform PDF is created from 0.2 to 1 mol/l. Since there are 16 mol of C in the canister (see Table 2-4) and the minimum value of the Cavity water volume is 90 litres, the maximum concentration of carbon in the canister interior would be 0.178 mol/l, below the lower limit of the PDF. This PDF ensures that there is no precipitation of organic carbon.

32

The PDF of carbon solubility in the canister interior is created giving the same weight to the inorganic and the organic forms. In 50% of the realisations carbon solubility is sampled from the PDF of the solubility of organic carbon and in 50% of the realisations carbon solubility is sampled from the PDF of the solubility of inorganic carbon. Table 4-6 summarises the PDFs and Figure 4-1 represents the cumulative distribution functions (CDF) for the solubilities inside the canister (in mol/l) for all the elements in the inventory, obtained with the method presented in this section. Table 4-6. Solubility limits (Sol) in canister interior (in mol/l). LU=log-uniform distribution.

Element Value in the Reference

Case

PDF for the PSA (log10-normal)

Mean value log10(Sol)

Standard deviation log10(Sol)

Minimum value

Maximum value

Ag I 5.1·10-6 -4.88 0.95 6.9·10-8 2.5·10-4

Am III 1.1·10-5 -6.25 1.17 1.2·10-9 2.7·10-5

Be II 4.4·10-6 -5.74 0.46 7.6·10-8 4.4·10-6

Cinorganic

(50% of realisations) Not

applicable -3.52 1.08 9.3·10-7 1.0·10-2

Cm III 1.1·10-5 -6.25 1.17 1.2·10-9 2.7·10-5

Mo VI 2.4·10-6 -6.98 1.87 1.1·10-11 1.0·10-2

Nb V 1.9·10-7 -4.65 1.38 1.9·10-8 1.0·10-2

Ni II 8.3·10-4 -5.00 1.30 1.2·10-8 8.3·10-4

Np IV 1.0·10-9 -9.04 0.33 6.8·10-11 1.3·10-8

Pa V 1.0·10-8 -8.54 0.55 8.4·10-11 1.0·10-6

Pd II 3.9·10-6 -5.32 0.32 3.7·10-7 1.2·10-5

Pu III 6.3·10-9 -9.82 0.84 1.3·10-12 3.0·10-8

Ra II 6.7·10-11 -9.20 1.12 1.6·10-12 8.7·10-5

Se –II 5.9·10-11 -8.46 1.22 5.9·10-12 3.4·10-7

Sm III 3.6·10-7 -6.92 0.96 6.1·10-10 1.2·10-5

Sn IV 6.3·10-8 -6.04 0.89 6.3·10-9 1.3·10-5

Sr II 7.4·10-4 -3.35 0.99 2.0·10-6 1.0·10-2

Tc IV 3.9·10-9 -8.45 0.32 2.8·10-10 1.5·10-8

Th IV 4.2·10-9 -8.42 0.55 1.1·10-10 8.8·10-7

U IV 2.4·10-8 -8.14 0.54 2.1·10-10 3.0·10-7

Zr IV 1.8·10-8 -7.83 0.30 1.2·10-9 9.2·10-7


Case PDF for the PSA

Corganic

(50% of realisations) unlimited LU (0.2 – 1)

Cl, I, Cs unlimited unlimited

33

Figure 4-1. Cumulative distribution functions (CDFs) of the solubility limits in the canister interior (mol/l).

For fission and activation products, the values in the Reference Case in Table 4-6 are the reference solubilities in brackish water in the canister interior. For actinides and daughters (that form decay chains) the values in the Reference Case are the highest solubility values calculated in the canister interior, buffer porewater and backfill porewater for brackish water.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Solubility limits in the canister interior (mol/l)

Cu

mu

lati

ve p

rob

abili

ty

Sr

Pd

Nb

Sn

Ag

Zr

Be

Sm

Se

Tc

Mo

Ni

C

Fission and activation products

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Solubility limits in the canister interior (mol/l)

Cu

mu

lati

ve p

rob

abili

ty

URa

Pa

Np

AmCm

Th

PuActinides and

daughters

34

Log-normal distributions For a normal distribution 68% of the distribution is in the interval μ±σ, 95% of the distribution is in the interval μ±2σ, and 90% of the distribution is in the interval μ±1.845σ, where μ is the mean of the variable and σ is the standard deviation of the variable. In a log-normal distribution the logarithm of the variable is normally distributed. If μ is the mean of the logarithm (with base 10) of the variable and σ is the standard deviation of the logarithm (with base 10) of the variable, then: - 68% of the distribution is in the interval 10μ-σ to 10μ+σ - 95% of the distribution is in the interval 10μ-2σ to 10μ+2σ, and - 90% of the distribution is in the interval 10μ-1.845σ to 10μ+1.845σ When describing log-normal distributions the terms Geometric Mean and Geometric standard deviation (SD) can be used also, and are related with the μ and σ of the logarithm (with base 10) of the variable

10 10

4.2.3 Solubility limits at other locations

Table 4-2 to Table 4-5 provide information on the solubility limits for all the chemical elements for six groundwater compositions at 4 locations in the near field: - inside the canister, - at the groundwater/buffer interface, - in the buffer porewater and - in the backfill porewater. For a given groundwater composition, many chemical elements have identical or similar solubilities at the 4 locations, while for other elements the solubilities can be very different. Solubilities inside the canister are the boundary conditions for the transport through the small hole (or the enlarged hole) in the canister into the bentonite buffer. Since transport through the canister hole, the buffer and the backfill is controlled by diffusion, there will exist a concentration gradient in the near field, with the highest concentration happening in the canister interior. As a consequence, the solubility limits outside the canister can be reached only if they are smaller than the solubility limits in the canister interior. Sections 4.2.4 to 4.2.6 identify the chemical elements whose solubilities outside the canister can be significantly smaller than inside the canister, and how their reduced solubilities have been included in the PSA.

35

4.2.4 Solubility limits at the groundwater/buffer interface

In the transport model used in TURVA-2012 and previous assessments it is conservatively assumed that, if solubility limits at the groundwater/buffer interface are lower than in the buffer, any precipitates that are formed could well be transported as eigencolloids into the geosphere, where they would re-dissolve as concentrations drop below the solubility limits again. The abundance and fate of any colloids (natural of produced by the buffer) present at the groundwater/buffer interface represent modelling uncertainties that are treated conservatively omitting any possible solute precipitation in this region of the near field. Table 4-7. Solubility limits at the groundwater/buffer interface divided by solubility limits inside the canister for six groundwater compositions. The meaning of the blue cells is explained in the text.

Elements

Groundwater

Minimum Saline Brackish

Dilute carbonate

Brine KR4/861/1

High alkaline

Glacial water

Ag I 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00

Am III 6.5E+00 8.7E-01 1.2E+00 2.5E+00 1.0E+00 7.0E-01 7.0E-01

Be II 4.5E+00 1.6E+00 1.4E+00 4.4E+00 1.0E+00 1.2E+00 1.0E+00

Cinorg 1.5E+00 1.5E+00 1.0E+00 4.2E+00 1.0E+00 7.6E-01 7.6E-01

Cm III 6.5E+00 8.7E-01 1.2E+00 2.5E+00 1.0E+00 7.0E-01 7.0E-01

Mo VI 2.8E-03 9.6E-03 3.3E-01 1.0E-01 9.8E-01 9.9E-01 2.8E-03

Nb V 1.6E-01 6.3E-01 7.1E-01 1.9E-01 1.9E+00 2.2E+00 1.6E-01

Ni II 1.6E+01 2.5E+00 1.9E+00 2.3E+01 1.0E+00 8.6E-01 8.6E-01

Np IV 9.6E-01 1.0E+00 1.1E+00 1.0E+00 1.0E+00 1.0E+00 9.6E-01

Pa V 1.0E+00 1.0E+00 1.1E+00 1.7E+00 4.9E-01 4.2E+00 4.9E-01

Pd II 1.1E+00 1.0E+00 1.0E+00 1.3E+01 1.0E+00 1.0E+00 1.0E+00

Pu III 6.2E+01 2.6E+01 3.2E+00 2.8E+01 1.0E+00 1.0E+00 1.0E+00

Ra II 1.1E+02 1.0E+00 1.1E+00 9.6E-01 9.4E-01 9.8E-01 9.4E-01

Se -II 2.9E+00 8.3E+00 1.4E+00 1.5E+00 3.0E-02 2.2E+00 3.0E-02

Sm III 1.0E+01 1.5E+00 1.4E+00 1.8E+00 1.0E+00 8.9E-01 8.9E-01

Sn IV 5.4E-01 9.0E-01 9.1E-01 5.6E-01 1.0E+00 7.9E-01 5.4E-01

Sr II 3.8E+01 1.2E+00 1.0E+00 1.0E+00 1.0E+00 1.4E+00 1.0E+00

Tc IV 1.0E+00 1.0E+00 1.0E+00 9.6E-01 1.0E+00 1.1E+00 9.6E-01

Th IV 1.2E+00 1.5E+00 1.5E+00 1.1E+00 1.0E+00 9.0E-01 9.0E-01

U IV 8.0E-01 2.6E-01 2.1E+00 5.7E-01 5.0E-01 2.2E-01 2.2E-01

36

Although precipitation at the groundwater/buffer interface is not included in the calculation cases of [10] due to the uncertainties discussed in the previous paragraph, it will be included in the PSA. The PSA will provide information on the potential importance of precipitation at the groundwater/buffer interface. If the PSA finds that precipitation in this part of the near field has a negligible effect on radionuclide releases to the biosphere, it would be another argument for not including this process in the transport model. Table 4-7 presents the ratio “solubility at the groundwater/buffer interface” divided by “solubility inside canister” for the 6 groundwater compositions considered. The last column presents the minimum value of the ratio for each chemical element. A value of 5.0·10-3 mol/l is assigned to the “unlimited” solubilities in Table 4-2 and Table 4-3 to calculate the ratios. Table 4-7 shows that only for a few elements the solubility at the groundwater/buffer interface is much smaller than inside the canister at least for one of the six groundwaters considered, leading to a potential precipitation. When the solubility at the groundwater/buffer interface can be more than 4 times smaller than in the canister interior, the cell in the column “minimum” is shaded light blue. Four elements have a much smaller solubility at the groundwater/buffer interface than in the canister interior at least for one groundwater composition (more than a factor 4 of decrease). For U and Nb the difference is smaller than one order of magnitude while for Mo and Se the difference is greater. To include this effect in the PSA, the solubilities of these 4 elements at the groundwater/buffer interface (damaged rock in the spalled region) are defined as the product of the PDF for the solubility in the canister interior multiplied by another PDF (called Solubility reduction factor at the groundwater/buffer interface) that takes into account the possible reduction of solubility in that region of the near field. For each element the PDF of the solubility reduction factor is a Log-Uniform distribution from the “minimum” value in Table 4-7 (rounded to the lower order or half order of magnitude) to 1, and are shown in Table 4-8. For the remaining elements the solubility in the groundwater/buffer interface is the same that in the canister interior. Table 4-8. Solubility reduction factors at the groundwater/buffer interface. LU=log-uniform distribution

Element PDF for the PSA

Mo LU (10-3 - 1)

Nb LU (10-1 - 1)

Se LU (10-2 - 1)

U LU (10-1 - 1)

37

4.2.5 Solubility limits in the buffer

Table 4-9 presents the ratio “solubility in the buffer” divided by “solubility inside canister” for all the chemical elements and the six groundwater compositions considered. The last column shows the minimum value of the ratio for each chemical element. A value of 5.0·10-3 mol/l is assigned to the “unlimited” solubilities in Table 4-2 and Table 4-3 to calculate the ratios. Only for a few elements the solubility in the buffer can be much smaller than inside the canister, leading to a potential precipitation in a buffer. When the solubility in the buffer can be more than 4 times smaller than in the canister interior, the cell in the column “minimum” is shaded light blue.

Table 4-9- Solubility in the buffer divided by solubility inside the canister for six groundwater compositions. The meaning of the blue cells is explained in the text.

Elements

Groundwater


Dilute carbonate

Brine KR4/861/1

High alkaline

Glacial water

Ag I 3.0E+00 2.7E+00 1.4E+00 1.3E+00 1.0E+00 6.2E-01 6.2E-01

Am III 2.9E-01 1.1E+00 5.8E-01 3.4E-01 9.2E-01 1.0E+00 2.9E-01

Be II 1.4E+00 1.4E+00 8.6E-01 1.1E+00 1.1E+00 2.5E+00 8.6E-01

Cinorg 1.8E+00 8.2E-01 1.0E+00 3.3E+00 1.1E+00 1.1E+00 8.2E-01

Cm III 2.9E-01 1.1E+00 5.8E-01 3.4E-01 9.2E-01 1.0E+00 2.9E-01

Mo VI 1.1E-01 1.5E-02 8.1E-01 7.6E-02 9.8E-01 1.0E+00 1.5E-02

Nb V 6.4E-01 7.9E-01 1.2E+00 2.3E-01 1.9E+00 1.6E+00 2.3E-01

Ni II 2.0E+00 1.8E+00 8.3E-01 7.1E+00 1.0E+00 9.3E-01 8.3E-01

Np IV 9.1E-01 1.0E+00 1.0E+00 8.1E-01 1.0E+00 1.0E+00 8.1E-01

Pa V 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.1E+00 1.0E+00

Pd II 9.2E-01 1.0E+00 1.0E+00 2.4E+01 1.0E+00 1.0E+00 9.2E-01

Pu III 7.0E+00 1.3E+01 1.3E+00 4.1E+00 1.0E+00 1.0E+00 1.0E+00

Ra II 8.8E-01 7.2E-01 7.1E-01 1.1E+00 9.4E-01 5.7E-01 5.7E-01

Se -II 2.4E+00 7.3E+00 1.4E+00 1.8E+00 2.9E-02 8.3E-01 2.9E-02

Sm III 2.8E+00 1.8E+00 1.0E+00 3.6E-01 3.5E+00 9.5E-01 3.6E-01

Sn IV 7.6E-01 9.4E-01 1.1E+00 4.9E-01 9.2E-01 6.7E-01 4.9E-01

Sr II 7.7E+00 9.1E-01 2.8E+00 1.0E+00 6.4E-02 8.0E-01 6.4E-02

Tc IV 9.2E-01 9.7E-01 1.0E+00 7.9E-01 1.0E+00 1.0E+00 7.9E-01

Th IV 1.3E+00 8.6E-01 1.2E+00 8.5E-01 1.0E+00 1.0E+00 8.5E-01

U IV 8.5E-01 1.5E-01 1.3E+00 8.1E-01 1.0E+00 7.9E-02 7.9E-02

Zr IV 8.8E-01 9.4E-01 1.0E+00 8.2E-01 1.0E+00 1.0E+00 8.2E-01

Five elements have a much smaller solubility in the buffer porewater than in the canister interior at least for one groundwater composition (more than a factor 4 of decrease). For

38

U and Nb the difference is smaller than one order of magnitude while for Mo, Sr and Se the difference is greater.

To include this effect in the PSA, the solubilities of these 5 elements in the buffer porewater are defined as the product of the PDF for the solubility in the canister interior multiplied by another PDF (called Solubility reduction factor in buffer) that takes into account the possible reduction of solubility in the buffer. For each element the PDF of the solubility reduction factor is a Log-Uniform distribution from the “minimum” value in Table 4-9 (rounded to the lower order or half order of magnitude) to 1, and are shown in Table 4-10. For the remaining elements the solubility in the buffer is the same that in the canister interior.

Table 4-10- Solubility reduction factors in the buffer. LU=log-uniform distribution


Mo LU (10-2 - 1)

Nb LU (10-1 - 1)

Se LU (10-2 - 1)

Sr LU (3·10-2 - 1)

U LU (3·10-2 - 1)

4.2.6 Solubility limits in the backfill

Table 4-11 presents the ratio “solubility in the backfill” divided by “solubility inside canister” for the 6 groundwater compositions considered. The last column presents the minimum value of the ratio for each chemical element. A value of 5.0·10-3 mol/l is assigned to the “unlimited” solubilities in Table 4-2 and Table 4-3 to calculate the ratios. For some elements the solubility in the backfill can be much smaller than inside the canister, potentially leading to precipitation in the backfill. When the solubility in the backfill can be more than 4 times smaller than in the canister interior, the cell in the column “minimum” is shaded light blue. Eight elements have a much smaller solubility in the backfill than in the canister interior at least for one groundwater composition (more than a factor 4 of decrease). For U, Sn and Nb the difference is smaller than one order of magnitude while for Ra, Mo, Sr and Se the difference is greater. To include this effect in the PSA, the solubilities in the backfill of these eight elements are defined as the product of the PDF for the solubility in the canister interior multiplied by another PDF (called Solubility reduction factor in the backfill) that takes into account the possible reduction of solubility in the backfill. For each element the PDF of the solubility reduction factors is a Log-Uniform distribution from the “minimum” value in Table 4-11 (rounded to the lower order or half order of magnitude) to 1, and are shown in Table 4-12. For the remaining elements the solubility in the backfill is the same that in the canister interior.

39

Table 4-11. Solubility limits in the backfill divided by solubility limits in the canister interior for six groundwater compositions. The meaning of the blue cells is explained in the text.

Elements

Groundwater


Dilute carbonate

Brine KR4/861/1

High alkaline

Glacial water

Ag I 2.8E+00 2.0E+00 1.6E+00 1.2E+00 2.8E+00 1.1E+00 1.1E+00

Am III 5.9E+00 1.8E+00 4.4E+00 1.4E+00 1.0E+00 2.1E+01 1.0E+00

Be II 1.8E+00 1.3E+00 2.2E+00 2.3E+00 1.1E+00 8.0E-01 8.0E-01

Cinorg 6.9E-01 7.8E-01 3.4E-01 3.4E+00 1.5E+00 1.8E-01 1.8E-01

Cm III 5.9E+00 1.8E+00 4.4E+00 1.4E+00 1.0E+00 2.1E+01 1.0E+00

Mo VI 4.2E-02 2.0E-02 4.4E-01 1.2E-01 1.2E+00 6.1E-02 2.0E-02

Nb V 4.0E-01 7.9E-01 4.7E-01 2.7E-01 1.9E+00 7.7E-02 7.7E-02

Ni II 3.3E+00 2.0E+00 1.1E+01 5.6E+00 1.0E+00 1.0E+01 1.0E+00

Np IV 9.5E-01 1.0E+00 9.2E-01 9.0E-01 9.7E-01 9.9E-01 9.0E-01

Pa V 1.0E+00 1.0E+00 1.3E+00 1.0E+00 1.0E+00 5.4E-01 5.4E-01

Pd II 1.0E+00 9.7E-01 9.8E-01 1.3E+01 9.7E-01 9.8E-01 9.7E-01

Pu III 6.5E+00 1.5E+01 4.2E+00 2.9E+00 1.0E+00 1.0E+00 1.0E+00

Ra II 2.0E+00 4.8E-01 2.2E-01 4.0E-01 1.9E-02 4.0E-02 1.9E-02

Se -II 7.2E-01 4.7E+00 1.1E+00 6.2E-01 4.3E-03 7.3E-02 4.3E-03

Sm III 7.0E+00 2.0E+00 3.2E+00 9.2E-01 9.6E-01 1.4E+01 9.2E-01

Sn IV 6.7E-01 9.2E-01 8.2E-01 5.1E-01 1.1E+00 1.0E-01 1.0E-01

Sr II 2.8E+00 4.7E-01 7.2E-01 1.0E+00 7.6E-02 7.0E+00 7.6E-02

Tc IV 1.0E+00 9.7E-01 9.8E-01 8.2E-01 1.0E+00 9.5E-01 8.2E-01

Th IV 8.1E-01 8.3E-01 4.9E-01 8.4E-01 1.0E+00 8.1E-01 4.9E-01

U IV 7.6E-01 1.6E-01 6.0E-01 8.6E-01 9.7E-01 3.6E-01 1.6E-01

Table 4-12. Solubility reduction factors in the backfill. LU=log-uniform distribution.


C LU (10-1 - 1)

Mo LU (10-2 - 1)

Nb LU (3·10-2 - 1)

Ra LU (10-2 - 1)

Se LU (3·10-3 - 1)

Sn LU (10-1 - 1)

Sr LU (3·10-2 - 1)

U LU (10-1 - 1)

40

4.2.7 Comments

Sections 4.2.4 to 4.2.6 describe the methodology followed to include in the model used for the PSA the solubility limits outside the canister: in the buffer, the backfill and the groundwater/buffer interface. In the PSA, for most elements the solubility outside the canister is the same than in the canister cavity. For the remaining elements the solubility outside the canister is the product of the PDF of the solubility in the canister interior (Table 4-6) times the PDF of the “solubility reduction factor” in that region (Table 4-8, Table 4-10 and Table 4-12). With the previous definition, if the solubility at a given location outside the canister has a significant effect on model results the PSA will identify that both the solubility in the canister interior and the corresponding “solubility reduction factor” are important parameters. If the solubility in the canister interior controls the model result and there is no precipitation outside the canister or such precipitation is not relevant (e.g. if precipitation happens in the backfill while peak releases are controlled by the F- and DZ-paths the PSA will identify the “solubility reduction factor” as a non-important parameter. When radionuclides transport through a small hole in the canister, the concentrations inside the canister are always much greater than in the bentonite porewater at the mouth of the hole. For C-14, Cl-36 and I-129 it has been found that there are three orders of magnitude of difference. Data in sections 4.2.4 to 4.2.6 show that for any element and groundwater composition the solubility outside the canister is, at most, 400 times smaller than the solubility in the canister interior. As a consequence, if transport is through a small hole in the canister overpack, it is expected that no precipitation will happen outside the canister, and the “solubility reduction factors” in the buffer, the backfill and the groundwater/buffer interface will be non-relevant parameters. Only in the calculations in which the small hole grows, and a much greater hole is created in the canister, the solute concentrations inside the canister and the bentonite porewater can become similar, and the “solubility reduction factors” can have some effect on model results.

41

5 BUFFER DATA

Table 5-1 summarises the values and PDFs assigned to the transport parameters of the buffer. Table 5-1. Summary of transport parameters in the buffer. LU=log-uniform distribution.

Parameter Value used in the


Buffer grain density (kg/m3) 2760 Constant (2760)

Total porosity 0.43 Constant (0.43)

De for anions (m2/s) 7.8·10-12 LU (3·10-13 - 3·10-11)

De for Cs (m2/s) 1.0·10-9 LU (2·10-11 - 3·10-9)

De for Ra and Sr (m2/s) 1.3·10-10 LU (2·10-11 - 10-8)

De for rest of cations and neutrals (m2/s) 1.3·10-10 LU (2·10-11 - 2·10-10)

Porosity accessible for anions 0.08 LU (0.01 – 0.17)

Porosity accessible for cations/neutrals 0.43 Constant (0.43)

Distribution coefficients in the buffer (m3/kg) (see Table 5-5) (see Table 5-5)

There is little uncertainty in the values of three parameters: the grain density, the total porosity and the porosity accessible for cations/neutrals (that is assumed to be 100% of the porosity). Constant values are assigned to these parameters in the PSA.

5.1 Porosity accessible for anions and diffusion coefficients

The PDFs for effective diffusion coefficients and the porosity accessible are based on the information contained in section 8 of [11], and especially on the recommended values in Table 8-4 of [11], which is reproduced in Table 5-2. For the porosity accessible for anions a Log-Uniform distribution has been adopted that spans from the lowest (0.01) to the highest (0.17) value of the parameter for the 6 groundwaters in Table 5-2. For De of the anions in the buffer a Log-Uniform distribution has been adopted that spans from the lowest to the highest value of the parameter for the six groundwaters in Table 5-2, with some rounding. The resulting PDF covers two orders of magnitude: from 3·10-13 to 3·10-11 m2/s.

42

Table 5-2. Recommended De values, accessible porosities and, in case of Cs+, Sr2+ and Ra2+, lower limit Kd values for safety assessment (Table 8-4 of [11])..

The PDF for the effective diffusion coefficient of neutral species and cations (with the exception of Cs, Ra and Sr) has been created following a different approach, because Table 5-2 provides a single value for the six groundwater compositions: 1.3·10-10 m2/s. This is a conservative value that corresponds to the upper limit for De(HTO) in the range of the bounding dry density conditions (1410-1650 kg/m3) and is the same for the six groundwaters because De(HTO) is little sensitive to groundwater composition. In [11] for a buffer porosity of 0.43 (dry density of 1570 kg/m3) a best estimate value of De(HTO) of 9.5·10-11 m2/s is suggested on the basis of a regression analysis of all diffusion data measured at room temperature. The lower and upper limits of De(HTO) identified in [11] are 3.3·10-11 m2/s and 1.3·10-10 m2/s respectively, and are based on the scatter of experimental data in the range of the bounding dry densities. This uncertainty range of De(HTO) had been expanded to cover one order of magnitude (from 2·10-11 to 2·10-10 m2/s). As a summary, De of the neutral species and cations (with the exception of Cs, Ra and Sr) in the buffer is represented using a Log-Uniform distribution from 2·10-11 to 2·10-10 m2/s. Table 5-2 provides recommended values for the effective diffusion coefficient of Cs and Sr-Ra for six groundwaters. De values for Cs and Ra-Sr are calculated in [11] for the six groundwaters and in some cases are smaller than the recommended value of De(HTO): 1.3·10-10 m2/s. Using De values for the cations smaller than De(HTO) “conflicts with the general concept of cation diffusion” and hence in [11] it is recommended to use De(HTO) as the minimum diffusivity of cations (values of 1.3E-10 m2/s in italics in Table 5-2). For De(Cs) in the buffer the upper limit is defined as the highest value of De(Cs) in Table 5-2: 3·10-9 m2/s after rounding. For the lower limit for De(Cs) in the buffer the lower limit of the PDF for De(HTO) is used: 2·10-11 m2/s. A Log-Uniform distribution from 2·10-11 to 3·10-9 m2/s is adopted, covering the uncertainty in the main mechanism of Cs transport in the buffer:

Saline KR20/465/1

Brackish KR6/135/8

Dilute , carbonate

rich KR4/81/1

Brine KR4/861/1

High alkaline

Glacial m elt w ater

Anions

De (m2 s-1) 1.0E-11 7.8E-12 2.1E-12 3.2E-11 1.0E-11 3.7E-13

ε dif f . available 0.11 0.08 0.01 0.17 0.11 0.01

Sr, Ra

De (m2 s-1) 1.3E-10 1.3E-10 1.3E-09 1.3E-10 2.2E-10 1.0E-08

Kd (m3 kg-1) 2.5E-04 1.4E-03 1.4E-02 2.34E-05 3.0E-03 1.1E-01

ε dif f . available

Cs

De (m2 s-1) 3.0E-10 1.0E-09 2.1E-09 1.3E-10 1.4E-09 3.1E-09

Kd (m3 kg-1) 1.4E-02 4.7E-02 9.6E-02 5.3E-03 6.2E-02 1.4E-01


Neutral species and other cations

De (m2 s-1)


0.43

0.43

0.43

1.3E-10

43

- standard diffusion in porewater: 2·10-11 m2/s<De(Cs)<2·10-10 m2/s, - enhanced diffusion due to “surface diffusion” or any other process: 2·10-10

m2/s<De(Cs)<3·10-9 m2/s The PDF for De of Ra-Sr is defined in the same way than for caesium. The upper limit is the highest value of De(Ra-Sr) in Table 5-2: 10-8 m2/s. The lower limit for De(Cs) in the buffer is the lower limit of the PDF for De(HTO): 2·10-11 m2/s. A Log-Uniform distribution from 2·10-11 to 10-8 m2/s is adopted, covering the uncertainty in the main mechanism of Ra-Sr transport in the buffer: - standard diffusion in porewater: 2·10-11 m2/s<De(Ra-Sr)<2·10-10 m2/s, - enhanced diffusion due to “surface diffusion” or any other process: 2·10-10

m2/s<De(Ra-Sr)<10-8 m2/s.

5.2 Distribution coefficients

Kd´s in the buffer enter into the transport equation under the form of a “capacity factor” or a “retardation factor” defined as

1

where θ is the porosity of the buffer accessible for a given radionuclide and ρDRY is the dry density of the buffer. Only cationic species present a significant sorption on bentonite, and they can access to all the porosity (θ=0.43). The capacity and retardation factors calculated for different values of Kd are shown in Table 5-3. Table 5-3. Capacity factors and retardation factors in the bentonite buffer for θ=0.43 and different values of the distribution coefficient.

Kd (m3/kg) Capacity Factor

Retardation Factor

10-6 0.4315732 1.004

10-5 0.445732 1.037

10-4 0.58732 1.366

10-3 2.0032 4.659

10-2 16.162 37.6

10-1 157.75 366.8

1 1573.63 3659

10 15732.43 36587

100 157320.43 365861

1000 1573200.43 3658605

Table 5-3 shows that Kd values smaller than 10-5 m3/kg translate into capacity factors very similar to the porosity and retardation factors close to 1. As a consequence, Kd values equal or smaller than10-5 m3/kg are roughly equivalent to Kd=0.

44

5.2.1 Input data

Input data used to create the PDFs for the distribution coefficients in the buffer have been taken from chapter 10 of [11], and summarised in Table 5-4. For each chemical element the data used are: - the best estimates of Kd in the buffer for six groundwaters, - the smallest of the lower limits for Kd in the buffer for six groundwaters (“lower

limit” in Table 5-4), and - the greatest of the upper limits for Kd in the buffer for six groundwaters (“upper

limit” in Table 5-4). Table 5-4. Input data for the distribution coefficients (Kd´s) in the buffer (taken from [11]).

Best estimate Kd (m3/kg) Lower limit

Upper limit

Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.10E-02 0.0E+00 3.2E-01

Am III 5.00E+01 3.20E+01 7.90E+01 1.99E+01 1.37E+02 1.35E+02 4.0E+00 6.1E+02

Be II 3.90E+01 3.90E+01 1.20E+02 3.30E+01 4.20E+01 1.30E+02 2.6E-01 8.4E+02

Cinorg 1.90E-04 2.10E-04 5.10E-05 2.20E-03 1.89E-02 6.70E-04 1.9E-05 7.0E-02

Corg 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Cl 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Cm III 5.00E+01 3.20E+01 7.90E+01 1.99E+01 1.37E+02 1.35E+02 4.0E+00 6.1E+02

Cs 6.20E-02 2.10E-01 4.30E-01 2.40E-02 2.80E-01 6.20E-01 5.3E-03 2.8E+00

I 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Mo VI 7.50E-03 2.10E-02 7.50E-03 1.50E-02 1.50E-04 3.38E-04 7.2E-06 8.7E-02

Nb V 5.43E+00 5.43E+00 5.43E+00 5.43E+00 1.81E+00 1.81E+00 1.0E-01 7.1E+01

Ni II 3.40E-01 2.40E-01 5.70E-01 1.11E-01 3.15E+00 3.15E+00 9.5E-03 3.7E+01

Np IV 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 1.0E+01 4.0E+02

Pa V 8.10E+01 8.10E+01 8.10E+01 8.10E+01 8.10E+01 8.10E+01 1.4E+01 4.7E+02

Pd II 7.00E-01 2.70E-01 6.30E-01 5.00E-03 3.12E+00 3.14E+00 3.1E-04 5.1E+01

Pu III 2.20E+01 9.90E+01 6.60E+01 8.35E+01 2.28E+01 2.40E+01 3.7E+00 5.8E+02

Ra II 1.50E-03 8.70E-03 1.10E-01 1.40E-04 1.80E-02 8.50E-01 2.3E-05 6.8E+00

Se –II 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Sm III 1.80E+01 1.00E+01 3.40E+01 3.00E+00 8.81E+01 1.13E+02 2.1E-01 1.8E+03

Sn IV 3.10E+01 5.00E+01 3.90E+01 4.46E+01 2.41E-01 1.14E+00 3.8E-02 3.1E+02

Sr II 1.50E-03 8.70E-03 1.10E-01 1.40E-04 1.79E-02 8.50E-01 2.3E-05 6.8E+00

Tc IV 6.30E+01 6.30E+01 6.30E+01 6.30E+01 2.10E+00 2.10E+00 1.4E-01 4.0E+02

Th IV 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 1.4E+01 2.8E+02

U IV+VI 4.80E+01 5.20E+01 1.80E+01 6.21E+01 6.29E+01 5.60E-02 7.9E-03 4.0E+02

Zr IV 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 6.30E+01 5.0E+00 4.0E+02

45

5.2.2 PDFs for Kd´s in buffer

In order to represent the uncertainty in the distribution coefficients in the buffer log-normal PDFs have been generated. Since Kd data typically span several orders of magnitude a logarithmic distribution has been adopted to give similar weight to the different orders of magnitude covered by the PDF. Due to the significant amount of data available, the goal was to create a realistic probability distribution, with regions of values with a higher probability and other less likely values. Definition of the log-normal PDFs Table 5-4 provides the following information for each chemical element: - The best estimate of Kd in the buffer for 6 groundwaters (V1, V2, V3, V4, V5, V6), - The lower limit of the Kd in the buffer for any water (Lower limit) and - The upper limit of the Kd in the buffer for any water (Upper limit) For each element, Maximum is defined as the highest value of V1, V2, V3, V4, V5 and V6 and Minimum is defined as the lowest value of V1, V2, V3, V4, V5 and V6. The range of values of Kd in the buffer for the 6 groundwaters (Minimum to Maximum) covers the geochemical uncertainty of the parameter. In addition, the value of the solubility for a given groundwater composition is affected by some uncertainty (formal uncertainty). Assuming a factor 2 for this formal uncertainty, the “range of most probable values” would be from Minimum/2 to 2·Maximum. When creating the PDFs for the Kd´s in the buffer it is intended to give a much higher weight in the distribution to the region of most probable values [Minimum/2, 2·Maximum], with the values outside that range being far less probable. Since the range of values of Kd in the buffer typically span oven several orders of magnitude, log-normal distributions have been adopted, and defined in such a way that: - 90% of the CDF (as a minimum) corresponds to the “most probable values”, - 5% of the CDF (as a maximum) is smaller than Minimum/2, and - 5% of the CDF (as a maximum) is greater than 2·Maximum.

The mean of the log10 of the Kd in the buffer is defined as the central value (in logarithms) of the range of the best estimate values of Kd in the buffer in the 6 groundwaters:

12

The standard deviation of the log10 of the Kd in the buffer is defined in such a way that 90% of the probability corresponds to the region of most probable values

2 /2

2 ∗ 1.845, 0.27

46

To ensure that the “range of most probable values” used in the calculations covers at least one order of magnitude a minimum value of 0.27 for SD log10(Kd) is imposed in the previous definition. The resulting log-normal PDF is truncated to avoid sampling values beyond the upper and lower limits included in section 5.2.1 :

Note for carbon: Excel data file provides Kd values in the buffer both for organic (Kd=0 for the 6 groundwaters) and inorganic carbon: - For the Kd in buffer of inorganic carbon a Log-Normal distribution is created using

the Kd data for inorganic carbon in the buffer in the 6 groundwaters, as explained in the previous paragraphs.

- The Kd in the buffer for organic carbon a represented with a Log-Uniform PDF from 10-7 to 10-5 m3/kg. Table 5-3 shows that Kd values between 10-7 to 10-5 m3/kg are equivalent to Kd=0.

The PDF of Kd(C) in the buffer is created giving the same weight to the inorganic and the organic forms. In 50% of the realisations Kd(C) in the buffer is sampled from the PDF of Kd in the buffer of organic carbon and in the other 50% of the realisations is sampled from the PDF of Kd in the buffer of inorganic carbon. Note for silver: The best estimate value for Kd(Ag) in the buffer is zero for 5 of the groundwaters considered in section 5.2.1 and only for the glacial water there is sorption (Kd=0.021m3/kg). In addition, the highest value of Kd(Ag) in the buffer for any water is 0.32m3/kg. To take into account the possibility of silver sorption on the buffer the following PDF is adopted for Kd(Ag) in the buffer: - In 80% of the realisations the value is sampled from a Log-Uniform distribution

between 10-7 to 10-5 m3/kg. Table 5-3 shows that Kd values between 10-7 to 10-5 m3/kg are equivalent to Kd=0.

- In 20% of the realisations the value is sampled from a Log-Uniform distribution between 10-5 and 0.3 m3/kg.

47

Table 5-5. Distribution coefficients (Kd´s) in the buffer (in m3/kg). LU=log-uniform distribution.


Case


Mean value log10(Kd)

Standard deviation log10(Kd)

Minimum value

Maximum value

Am III 3.2·10 1.72 0.39 4.0 6.1·102

Be II 3.9·10 1.82 0.32 2.6·10-1 8.4·102

Cinorganic

(50% of realisations)Not applicable -3.01 0.86 1.9·10-5 7.0·10-2

Cm III 3.2·10 1.72 0.39 4.0 6.1·102

Cs 4.8·10-2 -0.91 0.55 5.3·10-3 2.8

Mo VI 2.1·10-2 -2.75 0.74 7.2·10-6 8.7·10-2

Nb V 5.4 0.50 0.29 1.4·10-1 7.1·10

Ni II 2.4·10-1 -0.23 0.56 9.5·10-3 3.7·10

Np IV 6.3·10 1.80 0.27 1.0·10 4.0·102

Pa V 8.1·10 1.91 0.27 1.4·10 4.7·102

Pd II 2.7·10-1 -0.90 0.92 3.1·10-4 5.1·10

Pu III 9.9·10 1.67 0.34 3.7 5.8·102

Ra II 1.4·10-3 -1.96 1.19 2.3·10-5 6.8

Sm III 10 1.30 0.57 2.1·10-1 1.8·103

Sn IV 5.0·10 0.54 0.79 3.8·10-2 3.1·102

Sr II 1.4·10-3 -1.96 1.19 2.3·10-5 6.8

Tc IV 6.3·10 1.06 0.56 1.4·10-1 4.0·102

Th IV 6.3·10 1.80 0.27 1.4·10 2.8·102

U IV 5.2·10 0.27 0.99 7.9·10-3 4.0·102

Zr IV 6.3·10 1.80 0.27 5.0 4.0·102



Ag I 0 80% of realisations LU (10-7 – 10-5) 20% of realisations LU (10-5 – 0.3)

Corganic

(50% of realisations)0 LU (10-7 – 10-5)

Cl, I, Se 0 Constant (0)

Table 5-5 summarises the PDFs and Figure 5-1 represents the cumulative distribution functions (CDF) for the Kd´s in the buffer (in m3/kg) for all the elements in the inventory, obtained with the method presented in this section. Column “value in the Reference Case” in Table 5-5 corresponds to the best estimate values of Kd in the buffer in brackish water in Table 5-4 for all the radionuclides, with the exception of Cs, Sr and Ra, whose Kd´s in the buffer are the recommended values for brackish water in Table 5-2.

48

Figure 5-1. Cumulative distribution functions (CDFs) of the distribution coefficients (Kd’s) in the buffer (m3/kg).

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Distribution coefficients in the buffer (m3/kg)

Cu

mu

lati

ve p

rob

abili

ty

Sr

Pd

Nb

Sn

Ag

Zr

Be

Sm

Tc

Mo

Ni

Cs

C


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Distribution coefficients in the buffer (m3/kg)

Cu

mu

lati

ve p

rob

ab

ilit

y

U

Ra Pa

NpTh

AmCm

PuActinides and

daughters

49

6 BACKFILL DATA

In the current reference backfill design [20] it is foreseen to use three different materials: the tunnel floor will consist of granules of Milos bentonite with a medium dry density, the centre of the tunnel will be filled with compacted Friedland clay blocks with a high density and finer grained pellets of Milos bentonite with lower density will be used to fill the remaining void spaces in the wall and the roof. Table 6-1 summarises the values assigned to the transport parameters of the tunnel backfill in the Reference Case, as well as the probability density functions (PDFs) for the Probabilistic Sensitivity Analysis (PSA). Table 6-1. Summary of transport parameters in the backfill. LU=log-uniform distribution.

Parameter Reference

case PDF for the PSA

Backfill grain density (kg/m3) 2780 Constant (2780)

Total porosity 0.38 Constant (0.38)

De for anions (m2/s) 7.39·10-12 LU (3·10-13 - 3·10-11)

De for Cs (m2/s) 9.47·10-10 LU (10-11 - 3·10-9)

De for Ra and Sr (m2/s) 9.47·10-11 LU (10-11 - 10-8)

De for rest of cations and neutrals (m2/s) 9.0·10-11 LU (10-11 - 2·10-10)

Porosity accessible for anions 0.07 LU (0.01 – 0.15)

Porosity accessible for cations/neutrals 0.38 Constant (0.38)

Distribution coefficients in the backfill (m3/kg) (see Table 6-5) (see Table 6-5)

There is little uncertainty in the values of three parameters: the grain density, the total porosity and the porosity accessible for cations/neutrals (that is assumed to be 100% of the porosity). Constant values are assigned to these parameters in the PSA.

50

6.1 Diffusion coefficients and accessible porosity for anions

In the report on “Radionuclide solubility limits and migration parameters for the backfill” [12] it is stated that “to our knowledge, there are no diffusion data for Friedland clay or whole Milos bentonite. …Because of the lack of reference data regarding diffusion as well as actual properties (of the emplaced backfill), De values for the backfill were derived by scaling De values derived for similar material. For this purpose, the values derived in [11] (for the buffer material) are an obvious choice”. In [11], for De(HTO) in the buffer a best estimate value of 9.5·10-11 m2/s at the reference dry density of 1,570 kg/m3 (θ=0.43) is obtained on the basis of experimental values of De(HTO) in compacted montmorillonite and bentonite. In [12] “in the absence of any other evidence, the same dependency of De on dry density as in case of the buffer is assumed”, and for the reference dry density of 1720 kg/m3 (θ=0.38) a value of De(HTO)= 9.0·10-11 m2/s in the backfill is obtained (the same De(HTO) of the buffer with ρDRY=1720 kg/m3) As a consequence, the best estimate for De(HTO) in the backfill is 0.947 times the best estimate for De(HTO) in the buffer, and this scaling factor is used to derive most of De values in the backfill. In addition, in [12] a pessimistic value for De(HTO) in the backfill of 2.0·10-10 m2/s is proposed in view of the lack of diffusion data for the specified backfill material. The equivalent pessimistic value for De(HTO) in the buffer is 1.3·10-10 m2/s (section 5.1 ). The recommended values of De in the backfill given in [12] (Table 6-2) are closely based on the recommended values of De in the buffer given in [11] (Table 5-2): - for anions the scaling factor (based on the differences in dry densities of the buffer

and the backfill) is used for the six groundwaters, and De in the backfill is always 0.947 times the De in the buffer

- for neutral species and cations (with the exception of Cs, Ra and Sr) the best estimate value of De(HTO) in the backfill is recommended for the 6 groundwaters: 9.0·10-11 m2/s. It is noteworthy that the recommended value of De in the buffer for neutral species and cations (with the exception of Cs, Ra and Sr) is a pessimistic value of 1.3·10-10 m2/s that corresponds to the upper limit of De(HTO) in the range of the buffer bounding dry density conditions.

- for Cs, and Ra-Sr, if the recommended De value in the buffer for a given groundwater is 1.3·10-10 m2/s, then the recommended De value in the backfill is a pessimistic 2.0·10-10 m2/s (a factor 1.54 of difference). Otherwise, the recommended De value in the backfill is 0.947 times the recommended De value in the buffer.

51

Table 6-2. Recommended De values, accessible porosities and, in case of Cs+, Sr2+ and Ra2+, lower limit Kd values for safety assessment (Table 6-1 of [12]).

saline water KR20/465/1

brackish water KR6/135/8

dilute, carbonate rich water KR4/81/1

brine water KR4/861/1

high alkaline water

glacial melt water

Anions

De (m2/s) 9.47E-12 7.39E-12 1.99E-12 3.03E-11 9.47E-12 3.51E-13

diff 0.10 0.07 0.01 0.15 0.10 0.01

Sr, Ra

De (m2/s) 2.0E-10 2.0E-10 1.23E-09 2.0E-10 2.08E-10 9.47E-09

diff 0.38 0.38 0.38 0.38 0.38 0.38

Kd (m3/kg) 5.9E-04 9.8E-04 2.4E-03 3.8E-05 6.3E-04 3.7E-03

Cs

De (m2/s) 2.84E-10 9.47E-10 1.99E-09 2.0E-10 1.33E-09 2.94E-09

diff 0.38 0.38 0.38 0.38 0.38 0.38

Kd (m3/kg) 0.13 0.61 0.55 0.40 1.05 6.60

HTO, other cations, neutral species

De (m2/s), best estimate 9.0E-11 9.0E-11 9.0E-11 9.0E-11 9.0E-11 9.0E-11

De (m2/s), upper limit 2.0E-10 2.0E-10 2.0E-10 2.0E-10 2.0E-10 2.0E-10

diff 0.38 0.38 0.38 0.38 0.38 0.38

It is observed that for cations and neutral species there is a factor 0.623 or 0.947 of difference between the recommended values of De in the buffer and the backfill in most cases. For this reason the PDFs for De in the backfill for cations and neutral species are the same than for the buffer but with the lower limit divided by 2. For anions the factor of difference between the recommended values of De in the backfill and the buffer is always 0.947, very close to 1, and hence the PDF adopted for De in the backfill is the same than for De the buffer. Due to the lack of data for Friedland clay or whole Milos bentonite, the recommended values of accessible porosity for anions in the backfill in [12] (Table 6-2) were obtained scaling from the values proposed in [11] (Table 5-2) for the buffer. The scaling factor is the ratio of total porosities in both materials (0.38/0.43=0.88). For the porosity accessible for anions in the backfill a Log-Uniform distribution has been adopted, that spans from the lowest (0.01) to the highest (0.15) value of the parameter for the six groundwaters in Table 6-2.

52

6.2 Longitudinal dispersion in the backfill

The advective transport in the tunnel backfill induces a longitudinal dispersion that must be considered in the calculations. The diffusive-dispersive flux in a porous medium is

where De is the effective diffusion coefficient, αL is the dispersivity of the backfill and q is the Darcy velocity in the backfill. From the ConnectFlow results we know that the Darcy velocity values are between 10-7 and 10-3 m/a (3·10-15 to 3·10-11 m/s). For Boom clay the dispersivity value of 0.004m is used in [5]. A dispersivity of 1cm would translate into a factor αL·q between (3·10-17 to 3·10-13 m2/s). Taking into account the ranges of values adopted for the effective diffusion coefficients in the backfill it is observed that:

- for all the cationic and neutral species than De in the backfill is at least two orders of magnitude smaller than the longitudinal dispersivity in the tunnel, and

- for anions the longitudinal dispersion in the tunnel is similar to De in the backfill when Darcy velocity takes the maximum value and De the minimum value. When both parameters are sampled independently, De in the backfill will be much greater than the longitudinal dispersion in the tunnel in most realisations.

As a consequence, in the tunnel backfill the effect of longitudinal dispersion is negligible compared with diffusion, and is not included in the model.

53

6.3 Distribution coefficients

Distribution coefficients (Kd´s) in the backfill enter into the transport equation under the form of a “capacity factor” or a “retardation factor” defined as

1

where θ is the porosity of the backfill accessible for a given radionuclide. Only non-anionic species present a significant sorption on the backfill, and they can access to all the porosity (θ=0.38). The capacity and retardation factors calculated for different values of Kd are shown in Table 5-3. Table 6-3 shows that Kd values of 10-5 m3/kg or smaller translate into capacity factors very similar to the porosity (θ=0.38) and retardation factors close to 1. As a consequence, Kd≤10-5 m3/kg are roughly equivalent to Kd=0.

Table 6-3. Capacity factors and retardation factors in the backfill for θ=0.38 and different values of the distribution coefficient.

Kd (m3/kg) Capacity Factor

Retardation Factor

10-6 0.381724 1.005

10-5 0.397236 1.045

10-4 0.552360 1.454

10-3 2.103600 5.53

10-2 17.616 46.35

10-1 172.74 454.57

1 1723.98 4536.7

10 17236.38 45358.8

100 172360.38 453579.9

1000 1723600.38 4535790.4

54

6.3.1 Input data

Input data for the distribution coefficients (Kd’s) in the backfill have been taken from [12] and are summarised in Table 6-4. For each chemical element the data used are: - the best estimates of Kd in the buffer for six groundwaters, - the smallest of the lower limits for Kd in the buffer for six groundwaters (“lower

limit” in Table 6-4), and - the greatest of the upper limits for Kd in the buffer for six groundwaters (“upper

limit” in Table 6-4). Table 6-4. Input data for the distribution coefficients (Kd´s) in the backfill.

Best estimate Kd (m3/kg) Lower limit

Upper limit

Saline water

Brackish water

Dilute carbonate

water

Brine KR4/861/1

High alkaline

Glacial water

Ag I 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.48E-02 0.0E+00 2.2E-01

Am III 1.19E+02 1.78E+02 2.24E+02 7.50E+01 2.42E+02 9.20E+01 2.0E+00 4.4E+02

Be II 5.20E+01 5.20E+01 1.04E+02 4.61E+01 5.47E+01 1.10E+02 2.0E-01 7.0E+02

Cinorg 1.60E-03 6.90E-04 3.50E-04 7.30E-03 4.40E-02 1.30E-02 1.3E-04 1.6E-01

Corg 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Cl 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Cm III 1.19E+02 1.78E+02 2.24E+02 7.50E+01 2.42E+02 9.20E+01 2.0E+00 4.4E+02

Cs 7.84E-01 3.66E+00 3.29E+00 2.40E+00 6.29E+00 3.96E+01 1.3E-01 2.4E+02

I 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 5.0E-04

Mo VI 9.60E-03 1.90E-02 1.90E-02 1.20E-02 1.30E-04 9.60E-04 6.2E-06 8.0E-02

Nb V 3.00E+00 3.00E+00 3.00E+00 3.00E+00 1.00E+00 1.00E+00 3.0E-01 2.0E+01

Ni II 1.00E+00 1.50E+00 1.20E+00 7.00E-01 6.30E+00 4.00E+00 1.0E-01 3.7E+01

Np IV 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 2.0E+00 6.4E+02

Pa V 5.70E+01 5.70E+01 5.70E+01 5.70E+01 5.70E+01 5.70E+01 1.0E+01 3.3E+02

Pd II 1.90E+00 1.90E+00 2.00E+00 5.00E-02 6.60E+00 5.90E+00 9.0E-03 3.8E+01

Pu III+IV 2.05E+02 1.87E+02 1.37E+02 3.38E+02 1.15E+02 1.21E+02 4.0E+00 6.7E+02

Ra II 3.53E-03 5.86E-03 1.90E-02 2.26E-04 3.80E-03 2.96E-02 3.8E-05 2.4E-01

Se -II 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.0E+00 0.0E+00

Sm III 3.60E+01 4.90E+01 5.40E+01 1.10E+01 4.80E+01 2.70E+01 1.0E+00 3.2E+02

Sn IV 1.01E+02 1.01E+02 1.01E+02 1.01E+02 1.01E+02 1.01E+02 1.4E+01 4.6E+02

Sr II 3.53E-03 5.86E-03 1.90E-02 2.26E-04 3.80E-03 2.96E-02 3.8E-05 2.4E-01

Tc IV 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.0E+00 6.4E+02

Th IV 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 4.0E+00 6.4E+02

U IV+VI 1.10E+02 1.10E+02 7.30E+01 1.10E+02 1.10E+02 1.10E+02 2.0E+00 6.4E+02

Zr IV 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 1.10E+02 2.0E+00 1.2E+03

55

6.3.2 PDFs for Kd´s in backfill

In order to represent the uncertainty in the distribution coefficients in the backfill log-normal PDFs have been created. Since Kd data typically span over several orders of magnitude a logarithmic distribution has been adopted to give similar weight to the different orders of magnitude covered by the PDF. Due to the significant amount of data available, it has been tried to create realistic probability distributions with regions of values with a higher probability and other less likely values.

Definition of the log-normal PDFs Section 6.3.1 provides the following information for each chemical element: - The best estimate of Kd in the backfill for 6 groundwaters (V1, V2, V3, V4, V5, V6), - The lower limit of the Kd in the backfill for any water (Lower limit) and - The upper limit of the Kd in the backfill for any water (Upper limit)

For each element, Maximum is defined as the highest value of V1, V2, V3, V4, V5 and V6 and Minimum is defined as the lowest value of V1, V2, V3, V4, V5 and V6. The range of values of Kd in the backfill for the 6 groundwaters (Minimum to Maximum) covers the geochemical uncertainty of the parameter. In addition, the value of Kd in the backfill for a given groundwater composition is affected by some uncertainty (formal uncertainty). Assuming a factor 2 for this formal uncertainty, the “range of most probable values” would be from Minimum/2 to 2·Maximum.

When creating the PDFs for the Kd´s in the backfill it is intended to give a much higher weight in the distribution to the region of most probable values [Minimum/2, 2·Maximum], with the values outside that range being far less probable. Since the range of values of Kd in the backfill typically span oven several orders of magnitude, log-normal distributions have been adopted, and defined in such a way that - 90% of the CDF (as a minimum) corresponds to the “most probable values”, - 5% of the CDF (as a maximum) is smaller than Minimum/2, and - 5% of the CDF (as a maximum) is greater than 2·Maximum.

The mean value of the log10 of the Kd in the backfill is defined as the central value (in logarithms) of the range of the best estimate values of Kd in the backfill in the 6 groundwaters:

12

The standard deviation of the log10 of the Kd in the backfill is defined in such a way that 90% of the probability corresponds to the region of most probable values

2 /2

2 ∗ 1.845, 0.27

To ensure that the “range of most probable values” used in the calculations covers at least one order of magnitude a minimum value of 0.27 for SD log10(Kd) is imposed in the previous definition.

56

The resulting log-normal PDF is truncated to avoid sampling values beyond the upper and lower limits included in section 6.3.1 :

Note for carbon: section 6.3.1 provides Kd values in the backfill both for organic (unlimited for the 6 groundwaters) and inorganic carbon. - For the Kd in backfill of inorganic carbon a log-normal distribution is created using

the data of inorganic carbon Kd in the buffer in the 6 groundwaters, as explained in the previous paragraphs.

- For the Kd in the backfill of organic carbon a log-uniform PDF is created from 10-7 to 10-5 m3/kg.

- Table 6-3 shows that Kd values between 10-7 to 10-5 m3/kg are equivalent to Kd=0. The PDF of Kd(C) in the backfill is created giving the same weight to the inorganic and the organic forms. In 50% of the realisations Kd(C) in the backfill is sampled from the PDF of Kd in the backfill of organic carbon and in the other 50% of the realisations is sampled from the PDF of Kd in the backfill of inorganic carbon. Note for silver: The best estimate value for Kd(Ag) in the backfill is zero for 5 of the groundwaters considered in section 6.3.1 and only for the glacial water there is sorption (Kd=0.015m3/kg). In addition, the highest value of Kd(Ag) in the backfill for any water is 23m3/kg. To take into account the possibility of silver sorption on the backfill the following PDF is adopted for Kd(Ag) in the backfill: - In 80% of the realisations the value is sampled from a Log-Uniform distribution

between 10-7 to 10-5 m3/kg. - Table 6-3 shows that Kd values between 10-7 to 10-5 m3/kg are equivalent to Kd=0. - In 20% of the realisations the value is sampled from a Log-Uniform distribution

between 10-5 to 20 m3/kg. Note for iodine: The best estimate value for Kd(I) in the backfill is zero for the 6 groundwaters considered in section 6.3.1 , but the highest value of Kd(I) in the backfill for any water is 5·10-4 m3/kg. To take into account the possibility of iodine sorption on the backfill the following PDF is adopted for Kd(I) in the backfill: - In 80% of the realisations the value is sampled from a Log-Uniform distribution

between 10-7 to 10-5 m3/kg. - Table 6-3 shows that Kd values between 10-7 to 10-5 m3/kg are equivalent to Kd=0. - In 20% of the realisations the value is sampled from a Log-Uniform distribution

between 10-5 to 5·10-4 m3/kg. Table 6-5 summarises the probability density functions (PDFs) and Figure 6-1 represents the cumulative distribution functions (CDF) for the Kd in the backfill (in m3/kg) for all the elements in the inventory, obtained with the method presented in this section. The values in the backfill used in the Reference Case correspond to the best estimate values of Kd in the buffer in brackish water in Table 6-4 for all the radionuclides, with the exception of Cs, Sr and Ra, whose Kd´s in the backfill are the values for brackish water in Table 6-2.

57

Table 6-5. Distribution coefficients (Kd´s) in the backfill (in m3/kg). LU=log-uniform distribution.


Case


Mean value

log10(Kd)

Standard deviation log10(Kd)

Minimum value

Maximum value

Am III 1.8·102 2.13 0.30 2.0 4.4·102

Be II 5.5·10 1.85 0.27 1.8·10-1 7.0·102

Cm III 1.8·102 2.13 0.30 2.0 4.4·102

Cinorganic

(50% of realisations)Not applicable -2.41 0.73 1.3·10-4 1.6·10-1

Cs 3.7 0.75 0.62 1.3·10-1 2.4·102

Mo VI 1.9·10-2 -2.80 0.75 6.2·10-6 8.0·10-2

Nb V 3.0 0.24 0.29 3.0·10-1 2.0·10

Ni II 1.5 0.32 0.42 1.0·10-1 3.7·10

Np IV 1.1·102 2.04 0.27 2.0 6.4·102

Pa V 5.7·10 1.76 0.27 7.0 3.3·102

Pd II 1.9 -0.24 0.74 9.0·10-3 3.8·10

Pu III 1.9·102 2.29 0.29 4.0 6.7·102

Ra II 9.8·10-4 -2.59 0.74 3.8·10-5 2.4·10-1

Sm III 4.9·10 1.39 0.35 1.0 3.2·102

Sn IV 1.0·102 2.00 0.27 1.4·10 4.6·102

Sr II 9.8·10-4 -2.59 0.74 3.8·10-5 2.4·10-1

Tc IV 1.1·102 2.04 0.27 1.0 6.4·102

Th IV 1.1·102 2.04 0.27 4.0 6.4·102

U IV 1.1·102 1.95 0.27 2.0 6.4·102

Zr IV 1.1·102 2.04 0.27 2.0 1.2·103



I 0 80% of realisations LU (10-7 – 10-5)

20% of realisations LU (10-5 – 5·10-4)

Ag I 0 80% of realisations LU (10-7 – 10-5) 20% of realisations LU (10-5 – 20)

Corganic

(50% of realisations)0 LU (10-7 – 10-5)

Cl, Se 0 Constant (0)

58

Figure 6-1. Cumulative distribution functions (CDFs) of the distribution coefficients (Kds) in the backfill (m3/kg).

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Distribution coefficients in the backfill (m3/kg)

Cu

mu

lati

ve p

rob

abili

ty

Sr

Pd

Nb

Ag

SnTcZr

Be

Sm

Mo

Ni

Cs

I


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Distribution coefficients in the backfill (m3/kg)

Cu

mu

lati

ve p

rob

ab

ilit

y

U

Ra

Pa

NpTh

AmCm

PuActinides and

daughters

59

7 NEAR-FIELD FLOWS AND LENGTH OF DISPOSAL TUNNEL

In the Monte Carlo simulations used in the PSA the values of the three water flows leaving the near field (QF, QDZ and QTDF), the Darcy velocity in the tunnel (qTDZ) and the tunnel length are taken from file ps_r0_5000.csv. This is an output file of the groundwater flow modelling case ps_r0_5000, that gives flow related transport parameter for each deposition hole location, using hydrogeological boundary conditions corresponding to the year 5,000 AD. The groundwater flow model is implemented in the computer code Connectflow. In the Reference Case the values of these 5 parameters are those corresponding to hole location 381 in ConnectFlow file ps_r0_5000.csv. Note that the present repository layout provides for 20% more deposition hole locations than would be needed to accommodate the nominal 4,500 disposal canisters to be emplaced in the repository. These locations are each assigned a number, ranging from 1 to 5,391. The extra capacity of the present layout allows for the rejection of some potential locations during the process of final disposal, on the grounds of unsuitable rock properties, as defined by the Rock Suitability Classification (RSC) criteria [1]. ConnectFlow data file contains the results provided by the hydrogeological DFN (discrete fracture network) model for all 5391 potential deposition hole locations. For some locations the particles released from the near field to simulate the transport through the geosphere do not leave the near field and hence no data is available for one or more of the pathways in the far field (QF, QDZ and QTDF are greater than zero but the corresponding WL/Q is zero). After deleting these locations there remain 4830 holes. When the Rock Suitability Classification (RSC) criteria [1] are applied, another 112 hole locations are deleted (because are intersected by a hydrogeological zone and/or infiltration>0.1 l/min). The resulting ConnectFlow file contains the 4718 hole locations that satisfy the RSC criteria and for which all the data are available. Of these 4718 hole locations there are 876 with QF=0, 155 hole locations with QDZ=0 and 13 hole locations with qTDZ, QTDF and Tunnel Length equal to zero. For the 13 hole locations with Tunnel Length equal to zero in the ConnectFlow file, a value of 1.29m is used for Tunnel Length in the calculations, that corresponds to the minimum non zero value of Tunnel Length for the 4718 hole locations that satisfy the RSC and for which all the data is available deposition holes. For these 13 hole locations qTDZ=QTDF=0, and these values are used in the calculations. Figure 7-1 shows the cumulative distribution functions (CDFs) of the different near field flows and the flow through the tunnel backfill (qTDZ·14m2, where 14m2 is the cross-sectional area of the deposition tunnel) sampled in the 4718 hole locations selected. Figure 7-2 shows the CDF of the transport distance in the disposal tunnel (Tunnel length).

60

Table 7-1. Summary of near field flows and tunnel length.

Parameter Reference Case PDF for the PSA

Deposition hole location Location 381 in

ps_r0_5000.csv 4718 hole locations of the 5391 in ps_r0_5000.csv are considered

QF (m3/a) 6.14·10-3 CDF in Figure 7-1 (min=0 max=2.85·10-2)

QDZ (m3/a) 2.69·10-4 CDF in Figure 7-1 (min=0 max=2.60·10-2)

QTDF (m3/a) 2.39·10-3 CDF in Figure 7-1 (min=0 max=3.63·10-2)

qTDZ (m/a) 2.56·10-5 CDF in Figure 7-1 represents qTDZ times

the tunnel section (14m2) (min=0 max=2.75·10-3)

Tunnel length (m) 5.84 CDF in Figure 7-2

(min=1.29m max=195.8m)

The three water flows leaving the near field (QF, QDZ and QTDF), the Darcy velocity in the tunnel (qTDZ) and the tunnel length are sampled independently, i.e. for a given realisation the values of these parameters do not correspond to a given hole in the ConnectFlow file. QF can correspond to hole 1233, QDZ can correspond to hole 334, and so on. Alternatively the hole location could be sampled and then use the values of the 5 parameters for that hole in the ConnectFlow file. Using this sampling scheme the values of the 5 parameters would be correlated, but for the purpose of the PSA (identify the important model parameters) is more appropriate to use uncorrelated input parameters, as discussed in Section 14.3 of [6]. Figure 7-3 shows that the CDFs of QF values at three different instants (2,000 AD, 3,000 AD and 5,000 AD) are nearly identical. A similar agreement is observed for the 4 other parameters, and for the geosphere transport parameters sampled from the ConnectFlow data file (see section 8 ). For these reasons, the ConnectFlow file used (ps_r0_2000.csv, ps_r0_3000.csv or ps_r0_5000.csv) is expected to have a negligible effect on the PSA results.

61

Figure 7-1. Cumulative distribution functions (CDFs) of the near field flows in the 4718 holes for which all data are available and satisfy the RSC criteria. Boundary conditions correspond to 5000 AD.

Figure 7-2. Cumulative distribution function (CDF) of the transport distance in the disposal tunnel in the 4718 holes for which all data are available and satisfy the RSC. Boundary conditions correspond to 5000 AD.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01

Near field flows (m3/year)

Cu

mu

lati

ve p

rob

abil

ity

QF

QDZ

QTDF

qTDZ·14m2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E+00 1.E+01 1.E+02 1.E+03

Transport distance in the disposal tunnel (m)

Cu

mu

lati

ve p

rob

ab

ilit

y

62

Figure 7-3. Cumulative distribution functions (CDFs) of near flow QF in the holes for which all data is available and satisfy the RSC criteria. Boundary conditions correspond to three different instants: 2000 AD, 3000 AD and 5000 AD.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01

Near field flow QF (m3/year)

Cu

mu

lati

ve p

rob

abil

ity

ps_r0_2000.csv(green)

ps_r0_5000.csv(red)

ps_r0_3000.csv(blue)

63

8 FLOW-RELATED GEOSPHERE PARAMETERS

Table 8-1 summarises the values assigned to the flow related geosphere parameters in the Reference Case, as well as the probability density functions (PDFs) for the Probabilistic Sensitivity Analysis. Table 8-1. Summary of flow related geosphere transport parameters. LU=log-uniform distribution. CDF= Cumulative Distribution Function.


Deposition hole location Location 381 in

ps_r0_5000.csv 3710 hole locations of the 5391 in ps_r0_5000.csv are considered

Water travel time for F-path (a) 1.81·101 CDF in Figure 8-2

(min=6.92 max=7.60·103)

WL/Q for F-path(a/m) 3.95·104 CDF in Figure 8-1

(min=1.35·104 max=9.61·107)

Length of F-path (m) 1.96·103 CDF in Figure 8-3

(min=7.49·102 max=6.20·104)

Water travel time for DZ-path (a) 1.48·101 CDF in Figure 8-2

(min=6.44 max=6.51·103)

WL/Q for DZ-path (a/m) 4.65·104 CDF in Figure 8-1

(min=1.15·104 max=6.37·107)

Length of DZ-path (m) 1.90·103 CDF in Figure 8-3

(min=7.27·102 max=6.19·104)

Water travel time for TDZ-path (a) 1.74·101 CDF in Figure 8-2

(min=6.81 max=5.39·103)

WL/Q for TDZ-path (a/m) 3.76·104 CDF in Figure 8-1

(min=1.43·104 max=6.15·107)

Length of TDZ-path (m) 2.00·103 CDF in Figure 8-3

(min=7.41·102 max=4.28·104)

Peclet number N/A (transport

through a DFN LU (2-200)

64

8.1 Parameters provided by ConnectFlow

Values of the water transport resistance (WL/Q), water travel time and transport length in the geosphere for the 3 geosphere paths (related to QF, QDZ and QTDZ) are taken from ConnectFlow file ps_r0_5000.csv, which corresponds to the conditions 5,000 years after present. As explained in Chapter 7 , of the 5391 hole locations in the ConnectFlow file, there are 4718 hole locations that satisfy the RSC criteria and for which all the data is available. These 4718 hole locations are used to sample the near field flows. In 1017 of these hole locations at least one of the near field flows (QF, QDZ and QTDZ) is zero and the corresponding geosphere pathway is not defined. There remain 3701 hole locations that satisfy the RSC and for which the 3 transport paths F-, DZ- and TDZ- in the geosphere (associated to release paths from the near field QF, QDZ and QTDF, respectively) are well defined. As a consequence, the values of the geosphere parameters will be sampled only from these 3701 deposition hole locations. The 9 geosphere parameters are sampled independently, i.e. for a given realisation the values of the WL/Q, Water transport times and Transport length do not correspond to a given hole in the ConnectFlow file. WL/Q for the F-path can correspond to hole 1233, WL/Q for the DZ-path can correspond to hole 334, and so on. Alternatively the hole location could be sampled and then use the values of the 9 parameters for that hole in the ConnectFlow file. Using this sampling scheme the values of the 9 parameters would be correlated, but for the purpose of the PSA is more appropriate to use uncorrelated input parameters, as discussed in Section 14.3 of [6]. ConnectFlow data file provides F-factors while Posiva model works with WL/Q, but the relationship between both parameters is trivial: WL/Q=F/2. ConnectFlow data file provides F-factors for the 4 different classes of fractures, defined on the basis of their retention potential (section 4.8 of [7]): - Fractures dominated by calcite; - Fractures dominated by hydrothermal clays; - Slickensided fractures and - Other fractures For the PSA the total WL/Q for the whole migration paths is used. Total WL/Q is defined as the sum of the F-factors for the 4 classes of fractures for a given migration path (DZ-path for hole location 1444, for instance) divided by 2. The resulting cumulative distribution functions (CDFs) for the transport resistances, water travel times and lengths of the geosphere pathways for the F-, DZ- and TDZ-paths are shown in Figure 8-1, Figure 8-2 and Figure 8-3, respectively.

65

Figure 8-4 shows that the CDFs for the transport resistance of the F-path at three different instants (2,000 AD, 3,000 AD and 5,000 AD) is very similar. Similar agreements are observed for the remaining 8 geosphere parameters sampled from the ConnectFlow file. In section 7 it was found that the CDFs of the near field flows in the ConnectFlow files for the three instants are very similar also. For these reasons the ConnectFlow file used (ps_r0_2000.csv, ps_r0_3000.csv or ps_r0_5000.csv) is expected to have a negligible effect on the PSA results.

66

Figure 8-1. Cumulative distribution functions of the transport resistance (WL/Q) for F-, DZ- and TDZ-paths. Data for 3701deposition holes. Boundary conditions corresponding to 5000 AD.

Figure 8-2. Cumulative distribution functions of the water travel times (tW) of the F-, DZ- and TDZ-paths. Data for 3701 holes. Boundary conditions corresponding to 5000 AD.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

Transport resistance WL/Q (a/m)

Cu

mu

lati

ve p

rob

abil

ity

TDZ-path (red)

DZ-path (green)

F-path (blue)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

Water travel time (years)

Cu

mu

lati

ve p

rob

ab

ilit

y

F-path (blue)

DZ-path (green)

TDZ-path (red)

67

Figure 8-3. Cumulative distribution functions of the lengths of the F-, DZ- and TDZ-paths. Data for 3701 deposition holes. Boundary conditions corresponding to 5000 AD.

Figure 8-4. Cumulative distribution functions of the transport resistance (WL/Q) for F-path with boundary conditions corresponding to three different instants: 2000 AD, 3000 AD and 5000 AD.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E+02 1.E+03 1.E+04 1.E+05Length of the geosphere path (m)

Cu

mu

lati

ve p

rob

abil

ity

DZ-path (green)

TDZ-path (red)

TDZ-path (red)

F-path (blue)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

Transport resistance (WL/Q) for F-path (a/m)

Cu

mu

lati

ve p

rob

abil

ity

ps_r0_5000.csv

ps_r0_2000.csv

ps_r0_3000.csv

68

8.2 Longitudinal dispersion (Peclet number)

The longitudinal dispersion coefficient in a fracture (DL) is defined as the product of the longitudinal dispersivity (αL) times the water velocity in the fracture (v). The longitudinal dispersivity is usually defined as proportional to the length of the transport path (L), and the constant of proportionality is the inverse of the Peclet number (Pe).

In SKB TR-10-52 [4] it is stated that “field evidence from tracer tests suggests that the longitudinal dispersivity typically is 10% of the distance of the tracer test; this yields a Peclet number of 10”. In [7] a constant value of Peclet number equal to 10 is selected to be used in SR-Site, with a path length of 500m and a longitudinal dispersivity of 50m. In the Reference Case the transport is the geosphere is done with MARFA using a complex DFN. Although no longitudinal dispersion is considered in the individual fractures, the transport from the deposition hole to the biosphere will take place through different paths leading to a time spread of the releases to be biosphere similar to the spread that longitudinal dispersion would produce in the transport through a single fracture. In the Monte Carlo simulations done with GoldSim for the PSA, for each of the 3 release paths from the near field (F-, DZ- and TDZ-paths) the transport through the geosphere is modelled using a 1D streamtube from the release point from the near field to the biosphere. GoldSim cannot perform transport calculations in the geosphere without longitudinal dispersion (Pe=infinite). The minimum longitudinal dispersivity in GoldSim calculations is 0.5% the length of the path (Pe=200) when using “medium precision”. Using “high precision” in GoldSim would allow performing calculations with dispersion equal to 0.1% of the length of the path (Pe=1000), that would be closer to the Reference Case, but computer time increases significantly and the sample size (number of realisations of the Monte Carlo simulation) available for the PSA would decrease. For the Peclet number a Log-Uniform PDF has been adopted from 2 (1/5th of the value of 10 commonly assigned to Pe) to 200 (the maximum value that can be handled by GoldSim using “medium precision”). The resulting PDF spans over two orders of magnitude.

69

9 UNALTERED ROCK PROPERTIES

Table 9-1 summarises the values assigned to the transport parameters of the unaltered rock in the Reference Case, as well as the probability density functions (PDFs) for the Probabilistic Sensitivity Analysis. Table 9-1. Summary of transport parameters in the unaltered rock. LU=log-uniform distribution. CDF=cumulative distribution function.


Unaltered rock grain density (kg/m3) 2700 Constant (2700)

Total porosity 0.005 LU (0.001 – 0.02)

De for all species (m2/s) 6·10-14 LU (10-15 - 10-12)

Maximum penetration depth in the unaltered rock(m)

3

20% of realizations LU (0.1 – 1)

80% of realizations LU (1.0 – 10)

CDF in Figure 9-2

Distribution coefficients in the unaltered rock (m3/kg)

See Table 9-6 See Table 9-6

Due to the small uncertainty in the grain density of the unaltered rock a constant value of 2700 kg/m3 is used in the PSA.

70

9.1 Porosity and diffusion coefficients

Figure 9-1 shows the effective diffusion coefficient and porosity measured from Olkiluoto, Kivetty and Palmottu rock samples using the He gas method [17]. Measured He gas diffusivities have been scaled to represent water-phase diffusivities of a neutral species that has a diffusivity of 2·10-9 m2/s in free water. The fitted line used to determine the diffusivities of the immobile zones is based only on Olkiluoto-specific data (OL and OL-KR12). Samples from the OL-KR12 represent altered host rock. The values of porosity in Figure 9-1 span from 0.0003 to 0.06, with a factor 200 of difference between the lowest and the highest values. Due to the heterogeneity of the granite, the properties of the unaltered rock in contact with the fractures will change along the transport pathway that communicates the repository with the biosphere, and with the depth into the unaltered rock. It is logical to assign average properties to the matrix of the 1D stream tube that represents the geosphere in transport model used in the Monte Carlo simulations for the PSA. This averaging of the granite porosity is done by SKB in TR-10-52 [4] also, and the experimental values of porosity in cm-scale samples present so little dispersion that a constant value of 0.18% is assigned to the unaltered granite porosity in the probabilistic calculations. For the PSA a relatively wide range of values of the matrix porosity is created dividing/multiplying by 5 the value used in the Reference Case (0.5%), and rounding the resulting upper value. A Log-Uniform distribution between 0.001 and 0.02 is adopted for the PSA. This range of values takes into account the wide range of values of the porosity measured in rock samples and the expected averaging along the transport path.

71

Figure 9-1. Effective diffusivity and porosity measured from Olkiluoto, Kivetty and Palmottu (Figure taken from [17].

Figure 9-1 shows the effective diffusion coefficient measured from Olkiluoto, Kivetty and Palmottu rock samples, with a range of values of De between 10-15 m2/s and 10-12 m2/s. In SKB TR-10-52 [4] relatively narrow distributions are assigned to De: 10-14 to 3·10-13 m2/s for cations/neutral species and 3·10-15 to 10-13 m2/s for anions (mean value±3σ). For the PSA the range of values of De in unaltered rock is based on the measured values, adopting a Log-Uniform distribution between 10-15 m2/s and 10-12 m2/s. In the calculation cases analysed in the Analysis of Release Scenarios [10] it is assumed that there is no anion exclusion in the unaltered rock, and the same porosity and De in unaltered rock are assigned to all the radionuclides.

72

9.2 Maximum penetration depth in the unaltered rock

The maximum penetration depth in the unaltered granite has been defined on the basis of the spacing of the fractures at depth. Assuming that transport takes place along several parallel fractures the maximum penetration depth would be half the fracture spacing. The same approach is followed in TR-10-52 [4] for SR-Site: ”Concerning the maximum penetration depth, it is argued in Section 6.8 that the matrix pore space is connected over all distances of interest within the assessment. The maximum penetration depth is given by the average fracture spacing….The maximum penetration depth is half the fracture spacing…”. The 5391 deposition holes in ConnectFlow file ps_r0_5000.csv intersect 11,299 transmissive fractures, which corresponds to an average of 2.096 fractures per deposition hole at repository depth (~420m). There are 4500 canisters to be disposed of in Olkiluoto, with different lengths of the deposition hole (DH): 1400 OL1&2 canisters (DH length 7.8 m), 750 LO1&2 canisters (DH length 6.6 m) and 2350 OL3&4 canisters (DH length 8.25 m). The 5319 potential deposition hole locations in the hydrogeological DFN model are distributed between the three classes of canisters in the same proportions, and the resulting mean length of the deposition hole is 7.835m. With the previous data fracture intensity at repository depth is 0.268 m-1, mean fracture spacing is 3.74m and the maximum penetration depth in the unaltered rock is 1.87m. Olkiluoto Hydrogeological Discrete Fracture Network Model [7] provides data on the intensity of transmissive fractures (called PFL fractures) for four depth zones: - Depth zone 1 (DZ1): elevation > -50 m; - Depth zone 2 (DZ2): -50 m > elevation > -150 m; - Depth zone 3 (DZ3): -150 m > elevation > -400 m; - Depth zone 4 (DZ4): -400 m > elevation. Table 9-2. PFL intensities calculated for pilot holes in each depth zone, with different minimum transmissivity limits (m-1) (Table 10-3 of [7]).

Minimum transmissivity DZ1 DZ2 DZ3 DZ4

No minimum transmissivity 1.619 0.346 0.349 0.186

Minimum transmissivity > 2·10-11 1.619 0.346 0.349 0.165

Minimum transmissivity > 1·10-10 1.619 0.335 0.203 0.098

Minimum transmissivity > 10-9 1.131 0.246 0.071 0.035

Table 9-2 provides the calculated PFL intensities for each depth zone with different transmissivity limits in Olkiluoto. When no minimum transmissivity is considered the PFL intensity below -50m is quite similar in DZ2, DZ3 and DZ4: between 0.2 and 0.35 m-1 (fracture spacing of 2.8 to 5.0 m and maximum penetration depth in the unaltered rock of 1.4 to 2.5m). These values are similar to the fracture intensity calculated in the previous paragraph on the basis of the data on the fractures intersected by all the deposition holes contained in ConnectFlow file ps_r0_5000.csv. It must be noted that

73

data in Table 9-2 comes from pilot holes with a diameter of 76mm while the deposition hole diameter (considered in the hydrogeological DFN model) is 1.75m. If a minimum transmissivity limit is imposed, the PFL intensity decreases when the threshold increases, especially in DZ3 and DZ4. The intensity of PFL fractures with transmissivities greater than 10-9 is around 0.05 m-1 in DZ3 and DZ4, which corresponds to a fracture spacing of 20m and a maximum penetration depth in the unaltered rock of 10m. Most transport resistance is provided by the deeper zones of granite with much faster transport through the uppermost 150m or 50m of formation. For this reason, the selection of the range of values for the maximum penetration depth in the unaltered rock is based mainly on fracture intensity data in DZ3 and DZ4. With the results obtained in the previous paragraphs, and assuming that radionuclides transport through transmissive fractures, the following values of the maximum penetration depth in the unaltered rock are selected: - A best estimate value of 1 to 2 m (similar of the 3m used in the Reference Case) - A maximum value of 10m Conservative assumption of radionuclides transport through all the fractures (not only through the transmissive fractures) would lead to much lower values of the maximum penetration depth in the unaltered rock: - Table 10-4 in [7] provides a total fracture intensity around 1 m-1 in DZ4, which

corresponds to a fracture spacing of 1m. The resulting maximum penetration depth in the unaltered rock would be 0.5m.

- Figure 4-9 and 4-12 in [7] show that the intensity of all fractures is about 5m-1 and 3 m-1 in the hydrozones (hydrogeologically active deformation zones) and outside the hydrozones, respectively. The intensity of all fractures is not varying with depth (depth range 0 to -1000m), contrarily to the transmissive fractures, which intensity decreases significantly with depth. The lower limit for the maximum penetration depth in the unaltered rock is 0.1m that corresponds to the transport through all the fractures in a hydrozone.

Since radionuclides are expected to be transported through transmissive fractures, and most transport resistance will be provided by the lower granite layers (elevation <-150m) in 80% of the realisations the maximum penetration depth in the unaltered rock is sampled from a Log-Uniform distribution between 1 and 10m. To take into account the possibility of transport through all the fractures in the granite, in 20% of the realisations the maximum penetration depth in the unaltered rock is sampled from a Log-Uniform distribution between 0.1 and 1m. The resulting cumulative distribution function of the maximum penetration depth in the unaltered rock is shown in Figure 9-2.

74

Figure 9-2. Cumulative distribution function of the maximum penetration depth in the unaltered rock.

The maximum value of the PDF created (10m) is similar to the 12.5m adopted in SKB TR-10-52 [4] for SR-Site. Due to the relatively high value of the maximum penetration depth in the unaltered rock in most realisations it is expected that the results will be very similar to the case of a matrix of infinite thickness.

9.3 Distribution coefficients in the unaltered rock

Kd´s in the granite enter into the transport equation through a “capacity factor” or a “retardation factor” defined as

1

where θ is the porosity of the unaltered rock and ρDRY is the dry density of the unaltered rock. Table 9-3 shows the values of the capacity and retardation factors for 2 values of rock porosity (10-3 and 10-2) and different values of Kd. It shows that Kd values smaller than 10-6 or 10-7 m3/kg (depending on θ value) are roughly equivalent to Kd=0, with capacity factors similar to the porosity and retardation factors close to 1. It can be concluded that values of Kd in the unaltered rock smaller than 10-7 m3/kg are equivalent to Kd=0.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-01 1.E+00 1.E+01Maximum penetration depth in unaltered rock (m)

Cu

mu

lati

ve p

rob

ab

ilit

y

75

Table 9-3. Capacity factors and retardation factors in the unaltered rock for different values of the porosity and the distribution coefficient.

Kd (m3/kg) θ=10-3 θ=10-2

CF R CF R

0 1.00E-03 1.0000 1.00E-02 1.00000

10-9 1.00E-03 1.0027 1.00E-02 1.00027

10-8 1.03E-03 1.027 1.00E-02 1.0027

10-7 1.27E-03 1.27 1.03E-02 1.027

10-6 3.70E-03 3.7 1.27E-02 1.27

10-5 2.80E-02 28 3.70E-02 3.7

10-4 2.71E-01 271 2.80E-01 28

10-3 2.70E+00 2701 2.71E+00 271

10-2 2.70E+01 27001 2.70E+01 2701

10-1 2.70E+02 270001 2.70E+02 27001

1 2.70E+03 2700001 2.70E+03 270001

9.3.1 Input data

The input data used for creating the PDFs for the Kd´s in unaltered rock are summarised in Table 9-4 and Table 9-5, and have been taken from: - POSIVA 2012-41 Safety case for the disposal of spent nuclear fuel at Olkiluoto:

Radionuclide migration parameters for the Geosphere [14] for five water compositions. Kd´s upper limits (Table 9-4) are taken from Tables A-5 and A-6 of [14], and the lower limits (Table 9-5) are taken from Tables A-19 and A-20 of [14].

- POSIVA 2013-01 Safety case for the disposal of spent nuclear fuel at Olkiluoto. Models and Data Report [23] for the brine.

Data used correspond to two different rocks: PGR (Olkiluoto pegmatitic granite) and T-MGN (Olkiluoto T-series mica gneiss) Samarium is not included in the aforementioned tables of [14], and the values assigned to Kd(Sm) in Table 9-4 and Table 9-5 are in all cases the same than for americium, as recommended in section 19.2.2 of [14]: “It is proposed that the best estimate Kd values of other Ln (III) (Sm) lanthanides and An(III) (Am, Cm) actinides for reference rocks are the same as for Eu in the same chemical conditions”. Input values of Kd´s for the brine water in Table 9-4 and Table 9-5 were scaled from those for the OLSR. The scaling is not the same for all the elements, as the scaling process takes into account the main sorbing species and the dependency of the sorption on the ionic strength and pH (OLSR has pH of 8.3 and the brine water, OL-KR4_865 has pH of 7.8). The scaling process and the resulting best estimate and lower limits for the Kd´s in unaltered rock for brine groundwater are presented in reference [15].

76

Table 9-4. Input data for the distribution coefficients (Kd´s) in unaltered rock (upper limits).

Element

Upper limit Kd (m3/kg) Best estimate for T-MGN

Brackish OLBA

Dilute carbonate

KR4

Saline 10 g/l

KR20_465_1

Saline 10 g/l, pH10

KR20_465_1,

Brine 50g/l (Scaled

from OLSR)

Glacial, pH 10 OLGA

Ag 5.0E-07 5.0E-06 3.8E-08 3.8E-08 1.3E-09 1.4E-04

Am(III) 3.0E+00 3.0E+00 3.0E+00 2.7E+00 1.2E+00 3.0E+00

Be 3.2E+00 3.2E+00 3.2E+00 3.2E+00 3.2E+00 3.2E+00

C inorg & org - - - - 0.0E+00 -

Cl(-I) 1.7E-06 1.0E-05 1.0E-06 0.0E+00 4.3E-08 2.0E-06

Cm(III) 3.0E+00 3.0E+00 3.0E+00 2.7E+00 1.2E+00 3.0E+00

Cs 9.0E-02 1.2E-01 9.5E-02 1.1E-01 2.7E-02 1.7E+00

I 5.0E-06 3.0E-05 3.0E-06 0.0E+00 1.3E-07 6.0E-06

Mo 1.5E-03 2.4E-03 2.3E-03 9.2E-04 2.8E-04 1.6E-03

Nb(V) 1.9E+00 1.9E+00 1.9E+00 1.9E+00 1.9E+00 1.9E+00

Ni(II) 1.1E-01 1.5E-01 7.0E-02 5.9E+00 6.0E-02 5.9E+00

Np(IV) 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00

Pa(V) 1.1E-01 1.1E-01 1.1E-01 6.0E-02 1.0E-01 1.8E+00

Pd(II) 1.1E-01 1.5E-01 7.0E-02 5.9E+00 6.0E-02 5.9E+00

Pu(III) 3.0E+00 3.0E+00 3.0E+00 2.7E+00 1.2E+00 3.0E+00

Pu(IV) - - - 1.2E+01 - 1.2E+01

Ra 6.0E-02 1.0E-01 4.0E-02 4.0E-02 2.3E-03 3.5E-01

Se(II) - - - - 0.0E+00 -

Se (IV) 7.9E-03 7.9E-03 4.3E-03 1.1E-03 - 7.6E-04

Se(VI) - - - - - -

Sm(III) * 3.0E+00 3.0E+00 3.0E+00 2.7E+00 1.2E+00 3.0E+00

Sn(IV) 1.0E+01 1.0E+01 1.0E+01 3.6E-02 4.0E+00 3.6E-02

Sr 6.0E-04 2.0E-03 3.0E-05 3.0E-05 1.2E-06 1.6E-02

Tc(IV) 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00 7.8E+00

Th(IV) 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00

U(IV)/U(VI) 8.0E-02 2.2E-02 8.0E-01 8.0E+00 8.0E+00 8.0E+00

Zr(IV) 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00 8.0E+00

(*) For samarium the Kd´s of Am/Cm are used.

77

Table 9-5. Input data for the distribution coefficients (Kd´s) in unaltered rock (lower limits).

Element

Lower limit Kd (m3/kg) Lower limit for PGR

Brackish OLBA

Dilute carbonate

KR4

Saline 10 g/l

KR20_465_1

Saline 10 g/l, pH10

KR20_465_1,

Brine 50g/l (Scaled

from OLSR)

Glacial, pH 10 OLGA

Ag 4.0E-10 4.0E-09 4.0E-11 4.0E-11 1.3E-12 1.0E-07

Am(III) 2.2E-03 2.2E-03 2.2E-03 2.0E-03 8.8E-04 2.0E-03

Be 4.0E-04 6.0E-04 2.4E-04 2.2E-02 7.0E-04 2.2E-02

C inorg & org - - - - 0.0E+00 -

Cl(-I) 2.0E-09 1.3E-08 1.3E-09 0.0E+00 4.4E-11 1.8E-09

Cm(III) 2.2E-03 2.2E-03 2.2E-03 2.0E-03 8.8E-04 2.0E-03

Cs 4.0E-04 6.0E-04 4.0E-04 4.0E-04 1.0E-04 7.8E-03

I 6.0E-09 4.0E-08 4.0E-09 0.0E+00 1.3E-10 5.4E-09

Mo 6.8E-08 2.6E-06 8.2E-08 9.4E-09 9.6E-09 1.9E-07

Nb(V) 1.2E-02 1.2E-02 1.2E-02 1.2E-02 1.2E-02 1.2E-02

Ni(II) 4.0E-04 6.0E-04 2.4E-04 2.2E-02 7.0E-04 2.2E-02

Np(IV) 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02

Pa(V) 3.4E-04 3.4E-04 3.4E-04 3.4E-04 3.4E-04 6.2E-03

Pd(II) 4.0E-04 6.0E-04 2.4E-04 2.2E-02 7.0E-04 2.2E-02

Pu(III) 2.2E-03 2.2E-03 2.2E-03 2.0E-03 8.8E-04 2.0E-03

Pu(IV) - - - 5.0E-02 - 5.0E-02

Ra 6.0E-05 8.0E-05 8.0E-04 8.0E-04 2.2E-06 3.0E-04

Se(II) - - - - 0.0E+00 -

Se (IV) 1.8E-05 5.2E-06 6.0E-06 1.8E-06 - 1.9E-06

Se(VI) - - - - - -

Sm(III) 2.2E-03 2.2E-03 2.2E-03 2.0E-03 8.8E-04 2.0E-03

Sn(IV) 4.0E-02 3.6E-02 4.2E-02 1.4E-04 1.4E-02 1.4E-04

Sr 4.0E-07 2.0E-06 2.0E-08 2.0E-08 1.0E-09 1.3E-05

Tc(IV) 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02

Th(IV) 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02

U(IV)/U(VI) 2.0E-04 3.8E-05 2.0E-03 2.0E-02 2.0E-02 2.0E-02

Zr(IV) 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02 2.0E-02

(*) For samarium the Kd´s of Am/Cm are used.

78

9.3.2 Definition of the PDFs

The input data used (Table 9-4 and Table 9-5) provide upper and lower limits for the Kd´s in unaltered rock for six groundwater compositions and two rock types. This information covers the spatial and time variation and the uncertainty in geochemical conditions (through the consideration of six different groundwaters) as well as the variation of rock type along the migration path. For some elements there are several possible redox states in the geosphere and Table 9-4 and Table 9-5 provide data for all of them. For a given chemical element, the lower limit of the Kd is defined as the minimum value of lower limits for all the groundwater compositions and redox states, and the upper limit of Kd is defined as the maximum value of the upper limit for all the groundwater compositions and redox states. The resulting lower and upper limits for the Kd´s in the unaltered rock for each chemical element are shown in Table 9-6. When creating the PDFs for the Kds in the unaltered rock, the upper limits in Table 9-6 are raised because they are based on best estimates, which can be expected to be affected by some uncertainty. There is some probability of the Kds taking values higher than the upper limits in Table 9-6. For this reason the higher extreme of the PDFs are obtained rounding the upper limits in Table 9-6 to the next higher order or half an order de magnitude, and then adding another half an order of magnitude. For example, for Ag the upper limit of 1.4·10-4 m3/kg is rounded to 3·10-4 m3/kg and then increased to 10-3 m3/kg to obtain the higher extreme of the PDF for Kd(Ag) in granite. On the other hand, the lower limits in Table 9-6 are true lower limits, and it is not expected that the Kd´s will take values below them. For this reason they are adopted as the lower extremes of the PDFs, after rounded to the immediate lower order or half an order of magnitude. There are few exceptions: - the extremely low Kd value of 1.3·10-12 m3/kg for Ag is truncated to 10-10 m3/kg

(results in Table 9-3 show that Kd values of 10-12 or 10-10 m3/kg are both equivalent to Kd=0), and

- when the lower limit in Table 9-6 is zero (Cl, I and Se) a lower extreme of 10-10 m3/kg is adopted for the PDF.

The values in the Reference Case have been taken from Table 6-12 of the Assessment of Radionuclide Release Scenarios [10], and correspond to the lower limits for T-MGN rock with brackish groundwater. Log-Uniform distributions are assigned to the Kd´s in unaltered rock for all the elements, spanning from the lower to the upper limits defined as explained in the previous paragraphs. The PDFs are summarised in Table 9-6 and graphically represented in Figure 9-3.

79

Table 9-6. Distribution coefficients (Kd´s) in the unaltered rock. LU=log-uniform distribution.


Case

Range of Kd values PDFs for the PSA

Lower limit Upper limit

Ag 0 1.3·10-12 1.4·10-4 LU (10-10 – 10-3)

Am 1.5·10-1 8.8·10-4 3.0 LU (3·10-4 – 30)

Be 5.5·10-3 2.4·10-4 3.2 LU (10-4 – 30)

C 0 0 0 0

Cl 0 0 1.0·10-5 LU (10-10 – 10-4)

Cm 1.5·10-1 8.8·10-4 3.0 LU (3·10-4 – 30)

Cs 5.4·10-2 1.0·10-4 1.7 LU (3·10-5 –10)

I 0 0 3.0·10-5 LU (10-10 – 3·10-4)

Mo 3.0·10-4 9.4·10-9 2.4·10-3 LU (3·10-9 – 10-2)

Nb 4.2·10-1 1.2·10-2 1.9 LU (10-2 – 10)

Ni 5.5·10-3 2.4·10-4 5.9 LU (10-4 – 30)

Np 4.0·10-1 2.0·10-2 8.0 LU (10-2 – 30)

Pa 2.2·10-2 3.4·10-4 1.8 LU (3·10-4 – 10)

Pd 5.5·10-3 2.4·10-4 5.9 LU (10-4 – 30)

Pu 1.5·10-1 8.8·10-4 1.2·101 LU (3·10-4 – 100)

Ra 3.0·10-3 2.2·10-6 3.5·10-1 LU (10-6 – 3)

Se 0 0 7.9·10-3 LU (10-10 – 3·10-2)

Sm 1.5·10-1 8.8·10-4 3.0 LU (3·10-4 – 30)

Sn 5.0·10-1 1.4·10-4 2.0·101 LU (10-4 – 100)

Sr 3.0·10-5 1.0·10-9 1.6·10-2 LU (3·10-10 – 10-1)

Tc 4.0·10-1 2.0·10-2 8.0 LU (10-2 – 30)

Th 4.0·10-1 2.0·10-2 8.0 LU (10-2 – 30)

U 1.6·10-2 3.8·10-5 8.0 LU (3·10-5 – 30)

Zr 4.0·10-1 2.0·10-2 8.0 LU (10-2 – 30)

80

Figure 9-3. Cumulative distribution functions (CDFs) of the distribution coefficients (Kds) in the unaltered rock (m3/kg).

For several elements the PDFs for Kd in the unaltered rock span many orders of magnitude due to the very different characteristics of the groundwaters and the rock types covered by the input data in section 9.3.1 . An extreme case is the PDF for Se, which covers a range of 8.5 orders of magnitude. The Log-Uniform distribution adopted for Kd(Se) in the unaltered rock allows an homogeneous sampling of the whole range of variation:

- Kd is between 10-10 and 10-7 m3/kg (which is roughly equivalent to Kd=0) in 35% of the realisations, and

- each order of magnitude between 10-7 and 3·10-2 m3/kg is sampled in 12% of the realisations.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

Distribution coefficients in unaltered rock (m3/kg)

Cu

mu

lati

ve p

rob

ab

ilit

y

Sr

Nb

SnAg

BeTcZr

Sm

Mo

NiPd

Cs

I

Se

Cl


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

Distribution coefficients in unaltered rock (m3/kg)

Cu

mu

lati

ve

pro

bab

ility

U

Ra

Pa

NpTh

Am

Pa

Cm

Actinides and daughters

81

10 GEOSPHERE-BIOSPHERE ACTIVITY CONSTRAINTS

In the PSA calculations [6] the biosphere is not included. Repository consequences are quantified through the total normalized release rates from the near field and to the biosphere, which are calculated in this way: - for each radionuclide, the activity release rate from the near field (or to the

biosphere) is divided by the corresponding activity release constraint established in Guide YVL D.5 [2], and summarised in Table 10-1.

- the previous ratios are summed over all the radionuclides.

Radionuclide-specific normalized release rates are also calculated in [6].

82

Table 10-1. Activity release constraints (Bq/a) used in the PSA [6]. Blue cells identify the radionuclides whose constraints are not taken from the Guide YVL D.5.

Radionuclide Constraint (Bq/a) Radionuclide Constraint (Bq/a)

Ag108m 3.0E+08 Pu238 3.0E+07

Am241 3.0E+07 Pu239 3.0E+07

Am243 3.0E+07 Pu240 3.0E+07

Be10 3.0E+08 Pu241 3.0E+07

C-14 3.0E+08 Pu242 3.0E+07

Cl-36 3.0E+08 Ra226 3.0E+07

Cm245 3.0E+07 Se79 1.0E+08

Cm246 3.0E+07 Sm151 1.0E+11

Cs135 3.0E+08 Sn126 1.0E+09

Cs137 1.0E+08 Sr90 3.0E+08

I129 1.0E+08 Tc99 3.0E+09

Mo93 3.0E+09 Th229 3.0E+07

Nb91 3.0E+08 Th230 3.0E+07

Nb92 3.0E+08 Th232 3.0E+07

Nb93m 3.0E+08 U233 3.0E+08

Nb94 1.0E+08 U234 3.0E+08

Ni59 3.0E+10 U235 3.0E+08

Ni63 3.0E+10 U236 3.0E+08

Np237 1.0E+08 U238 3.0E+08

Pa231 3.0E+07 Zr93 1.0E+10

Pd107 1.0E+11

The Guide YVL D.5 [2] provides the activity release constraints for most radionuclides in the inventory considered in the calculations (Table 2-1). But for the radionuclides not included in the Guide YVL D.5 [2] it has been necessary to derive their activity release constraints: - the activity release constraints for short lived Cs-137, Ni-63, Sm-151 and Sr-90 have

been taken from RNT-2008 [9]; - for Ag-108m, Be-10, Nb-91, Nb-92 and Nb-93m a conservative value of 3·108 Bq/a

(second lowest value in the Guide YVL D.5 [2] for fission and activation products) has been selected, and

- for Mo-93 it has been recommended the same geo-bio flux constraint as for Tc-99, taking into account the inventory and the dose conversion factors for ingestion.

83

11 REFERENCES

[1] McEwen, T. (ed.), Aro, S., Hellä, P. Kosunen, P., Käpyaho, A., Mattila, J., Pere, T. 2012. Rock Suitability Classification - RSC 2012. POSIVA 2012-24. Posiva Oy, Eurajoki. 220 p. (in English) ISBN 978-951-652-205-3 [2] STUK. Guide STUK-YVL D.5. [3] Werme L O, Johnson L H, Oversby V M, King F, Spahiu K, Granbow B and Shoesmith DW, 2004. Spent fuel performance under repository conditions: A model for use in SR-Can. SKB TR-04-19, Svensk Kärnbränslehantering AB. [4]SKB TR-10-52 Data report for the Safety Assessment SR-Site. [5] Modelling of cation concentrations in outflow of NaNO3 percolation experiments hrough Boom Clay cores. EXTERNAL REPORT SCK•CEN-ER-85. 08/EMa/P-54 December 2008. [6] Cormenzana, J. L. 2013. Probabilistic Sensitivity Analysis for the “Initial Defect in the Canister” Reference Model. Working Report 2013-25. Posiva Oy, Eurajoki. 532 p. (in English) [7] Hartley, L., Appleyard, P., Baxter, S., Hoek, J., Roberts, D., & Swan D. 2012. Development of a Hydrogeological Discrete Fracture Network Model for the Olkiluoto Site Descriptive Model 2011. Working Report 2012-32. Posiva Oy, Eurajoki. 540 p. (in English) [8] Johnson L H, Tait J C, 1997. Release of segregated nuclides form spent fuel. SKB TR-97-18, Svensk Kärnbränslehantering AB. [9] Nykyri. M., Nordman, H., Marcos, N., Löfman, J., Poteri, A. & Hautojärvi. A. 2009. Radionuclide Release and Transport – RNT-2008. POSIVA 2008-06. Posiva Oy, Eurajoki. 164 p. (in English) [10] Posiva Oy. 2012. Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Assessment of Radionuclide Release Scenarios for the Repository System 2012. POSIVA 2012-09. Posiva Oy, Eurajoki. 435 p. (in English) ISBN 978-951-652-190-2 [11] Wersin, P., Kiczka, M. & Rosch, D. Safety Case for the Disposal of Spent Fuel at Olkiluoto: Radionuclide Solubility Limits and Migration Parameters for the Canister and the Buffer. POSIVA 2012-39. Posiva Oy. ISBN: 978-951-652-219-0. (In Preparation) [12] Wersin, P., Kiczka, M., Rosch, D., Ochs, M., Trudel, D. Safety Case for the Disposal of Spent Fuel at Olkiluoto: Radionuclide Solubility Limits and Migration Parameters for the Backfill. POSIVA 2012-40. Posiva Oy. ISBN: 978-951-652-220-6. (In Preparation)

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[13] SKB TR-10-13 Spent nuclear fuel for disposal in the KBS-3 repository. December 2010. [14] Hakanen, M, Ervanne H., Puukko E., Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto: Radionuclide Migration Parameters for the Geosphere. POSIVA 2012-41. Posiva Oy. ISBN 978-951-652-221-3. (In Preparation) [15] Posiva Oy. 2013. Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Models and Data for the Repository System 2012. Posiva Oy, Eurajoki. 818 p. (In English) ISBN 978-951-652-233-6. [16] Johnson L H, McGinnes D F, 2002. Partitioning of radionuclides in Swiss power reactor fuels. NAGRA NTB 02-07, National Cooperative for the Disposal of Radioactive Waste, Switzerland. [17] Posiva Oy. 2012. Olkiluoto Site Description 2011. POSIVA 2011-02. Posiva Oy, Eurajoki. 1028 p. (in English). ISBN 978-951-652-182-7 [18] Yamaguchi I, Tanuma S, Yasutomi I, Nakayama T, Tanabe H, Katsurai K, Kawamura W, Maeda K, Katao H, Saigusa M, 1999. A study on chemical forms and migration behavior of radionuclides in hull wastes. Proceedings of the 7th International Conference on Waste Management and Environmental Remediation, ICEM ’99, Nagoya, Japan, 26-30 September 1999. New York: American Society of Mechanical Engineers. [19] SKB TR-09-26. Fission gas release data for Ringhals PWRs. September 2009. [20] Keto, P. Technical memo: Backfill materials and dry density. B+Tech (draft).

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[21] Johnson, L., Günther-Leopold, I., Kobler Waldis, J., Linder, H.P., Low, J., Cui, D., Ekeroth, E., Spahiu, K. & Evins, L.Z. 2012. Rapid aqueous release of fission products from high burn-up LWR fuel: Experimental results and correlations with fission gas release. Journal of Nuclear Materials. Vol. 420, no. 1-3, p. 54-62. [22] ANDRA 2009. ThermoChimie Project, mid-term report. Andra internal document available on request [23] Hellä, P., Pitkänen, P., Löfman, J., Partamies, S., Wersin, P., Vuorinen, U. & Snellman, M. 2013. Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Definition of Reference Groundwaters and Bounding Waters, and Buffer and Backfill Porewaters. Posiva Oy, Eurajoki. POSIVA 2014-xx. Posiva Oy (In Preparation).

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