Thermal Dimensioning of Olkiluoto Repository for Spent · PDF fileTHERMAL DIMENSIONING OF OLKILUOTO REPOSITORY FOR SPENT FUEL ABSTRACT This report contains the updated temperature

December 2012

Working Reports contain information on work in progress

or pending completion.

Kari Ikonen

Heikki Raiko

VTT

Working Report 2012-56

Thermal Dimensioning of OlkiluotoRepository for Spent Fuel

THERMAL DIMENSIONING OF OLKILUOTO REPOSITORY FOR SPENT FUEL ABSTRACT This report contains the updated temperature dimensioning of the KBS-3V type spent nuclear fuel repository in Olkiluoto for the fuel canisters, which are disposed at vertical position in the horizontal tunnels in a rectangular geometry according to the preliminary Posiva plan. This report concerns only the temperature dimensioning of the repository and does not take into account the possible restrictions caused by the rock mechanical restrictions of the rock. The dimensioning criterion is the maximum temperature on the canister/buffer interface, which due to very good conductivity of copper is practically constant all around the canister surface. The postulated dry conditions for thermal dimensioning are very un-likely to exist, especially in long-term. The normal expected condition is that the buffer around canisters is water-saturated within shorter time. For this reason it is justified to apply lower safety margin for the maximum temperature in dry conditions than in satu-rated condition when dimensioning the canister spacings in the repository. The maximum temperature on the canister-bentonite interface is limited to the design temperature of +100°C. For the reasons presented above and further, due to uncertain-ties in thermal analysis parameters (like scattering in rock conductivity or in predicted decay power) the nominal calculated maximum canister temperature is set to 95°C hav-ing a safety margin of 5°C. Correspondingly in saturated condition, which is more prob-able, maximum nominal temperature is set to 90°C. The nominal temperature is con-trolled by adjusting the space between adjacent canisters, adjacent tunnels and the pre-cooling time of the spent fuel affecting on the decay power of the canisters. For the Olkiluoto repository, the dimensioning was made assuming the canisters to be in rectangular panels of 900 canisters of BWR, VVER or EPR spent fuel. The analyses were performed for each fuel types with an initial canister power of 1700 W, 1370 W and 1830 W, respectively. These decay powers correspond to the average decay heat of the spent fuel with pre-cooling time of 32.9, 29.6 or 50.3 years for fuels with average burn-up of 40, 40 or 50 MWd/kgU, respectively. The analyses gave the resulting can-ister spacing (7.5-10.5 m), when the tunnel spacing was 25 m. Keywords: Spent nuclear fuel, repository, decay heat, temperature dimensioning

KÄYTETYN POLTTOAINEEN LOPPUSIJOITUSTILAN LÄMPÖTILAMITOITUS TIIVISTELMÄ Raportissa kuvataan korkea-aktiivisten BWR-, VVER- ja EPR-ydinpolttoaineiden lop-pusijoituksen (LS-tilan) kallioon synnyttämien lämpötilakenttien laskentatulokset, kun kapselit sijoitetaan KBS-3V-ratkaisun mukaisesti pystyasentoon suorakaiteen muotoi-seen paneeliin. Tämä raportti käsittelee vain loppusijoitustilan lämpötilamitoitusta ja se ei ota huomioon kalliomekaanisten rajoitusten mahdollista vaikutusta. Kapseleiden asennusvaiheessa olosuhteet ovat kuivat. Tunneleiden sulkemisen jälkeen pohjaveden vuotovirtausten vaikutuksesta kosteus vähitellen lisääntyy, mikä parantaa bentoniitin lämmönjohtavuutta. Bentoniitin turvotessa sen ja kapselin välinen asen-nusilmarako sulkeutuu ja lämmönsiirto ympäristöön paranee myös tästä syystä. Koste-usolosuhteiden muuttumista kapselin ympäristössä ajan mukana on vaikea ennustaa. Siksi kapseleiden etäisyysmitoitus tehdään kahdessa ääritapauksessa, kuivassa ja satu-roituneessa tilanteessa. Kuivat olosuhteet johtavat selvästi suurempaan kapseliväliin huonompien lämmönsiirtymisolosuhteiden takia. Mitoituskriteerinä on kapselin ja puskurin rajapinnan lämpötilan maksimi, joka kuparin erittäin hyvän lämmönjohtumisen takia on käytännössä vakio kaikkialla kapselin pin-nalla. Pitkäaikaistarkastelussa olosuhteiden pysyminen kuivina on epätodennäköistä. Siksi on perusteltua käyttää erilaista lämpötilan turvallisuusmarginaalia kuivassa ja sa-turoitununeessa tilanteessa tehtävässä etäisyysmitoituksessa. Kapselin ja bentoniitin rajapinnan maksimilämpötila rajoitetaan suunnitteluarvoon +100°C. Edellä esitetyistä syistä ja materiaalien lämpöteknisten epävarmuustekijöiden (kuten kallion lämmönjohtumiskertoimen hajonnan ja jälkitehon ennustettavuuden) ta-kia laskennalliseksi lämpötilaksi pitkäaikaistarkastelussa kuivassa epätodennäköisessä tapauksessa sallitaan 95°C, mikä merkitsee 5°C:een turvallisuusmarginaalia suunnittelu-arvoon nähden. Vastaavasti pitkäaikaistarkastelussa saturoituneessa edellistä todennä-köisemmässä tilanteessa laskennalliseksi lämpötilaksi sallitaan korkeintaan 90oC. Esiintyvään maksimilämpötilaan voidaan vaikuttaa mm. kapselien ja tunnelien välisillä etäisyyksillä sekä polttoaineen jäähdytysajalla ja siitä riippuvalla alkuteholla. Olkiluodon loppusijoitustilalle analysoitiin tapaus, jossa 900 kappaletta BWR-, VVER- ja EPR-kapseleita sijoitetaan yhteen suorakaiteen muotoiseen osastoon suunnitelman mukaisessa järjestyksessä tunneleittain tietyssä suunnassa edeten. Yksittäisen kapselin alkutehoksi asetettiin sijoitushetkellä 1700 W, 1370 W ja 1830 W esijäähdyttämällä BWR, VVER ja EPR-polttoaineita 32,9, 29,6 ja 50,3 vuotta (palamat 40, 40 ja 50 MWd/kgU). Tulokseksi saatiin tarvittava kapselien välinen etäisyys (7.5-10.5 m), kun tunneliväli oli 25 m. Avainsanat: Käytetty ydinpolttoaine, loppusijoitustila, jälkilämpö, lämpötilamitoitus

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TABLE OF CONTENTS ABSTRACT TIIVISTELMÄ SYMBOL LIST ............................................................................................................... 2 1 INTRODUCTION .................................................................................................... 3 2 INITIAL DATA ......................................................................................................... 5 2.1 Geometry of canister near-field ..................................................................... 5 2.2 Thermal-mechanical properties of materials ................................................. 6 2.3 Emissivity of air gap surface ......................................................................... 9 2.4 Exponential decay heat modelling ............................................................... 10 3 CALCULATION METHODOLOGY ....................................................................... 13 3.1 Analytical solution ...................................................................................... 13 3.2 Effective height of the canister .................................................................... 14 3.3 Evaluation of canister surface temperature in analytic line heat source analysis ........................................................... 16 3.4 Numerical solution ..................................................................................... 19 4 ANALYSIS OF CANISTER PANEL ...................................................................... 21 4.1 Definition of base case ................................................................................ 22 4.2 Dependence of maximum canister surface temperature on canister spacing .......................................................................................... 23 4.2.1 BWR fuel canisters in dry case ......................................................... 24 4.2.2 VVER 440 fuel canisters in dry case ................................................. 26 4.2.3 EPR fuel canisters in dry case .......................................................... 28 4.2.4 BWR fuel canisters in saturated case ............................................... 30 4.2.5 VVER 440 fuel canisters in saturated case ....................................... 32 4.2.6 EPR fuel canisters in saturated case ................................................ 34 4.3 Canister spacing causing maximum allowable canister surface temperature ................................................................................................. 35 4.4 Effect of various saturation degrees of bentonite buffer ............................. 40 4.5 Effect of changing canister distance on edge areas .................................. 42 4.6 Temperature interaction between panels ................................................... 42 4.7 Effect of inaccuracy of canister position ..................................................... 45 4.8 Quality control of the analyzing process .................................................... 46 4.8.1 Applied means for quality control ...................................................... 46 4.8.2 Comparison to SKB analyses ........................................................... 47 4.9 Sensitivity to various parameters ................................................................ 49 4.10 Reasoning of temperature margins ............................................................ 51 5 CONCLUSIONS .................................................................................................. 53 REFERENCES ....................................................................................................... 55 APPENDIX: Near and far field calibration with a single fuel canister .......................... 57

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SYMBOL LIST LATIN ALPHABET unit cv volumetric heat capacity [J/m3/K] d thermal diffusivity, d = λ /(ρc) [m2/s] erf error function [-] F view factor [-] H actual height of a canister [m] Heff effective height of line heat source [m] k heat flux reduction coefficient [-] P power [W] q thermal density [J/m3] R, r radius [m] r0 external radius of canister [m] T temperature [oC or K] T0 canister surface temperature [oC] T0b bentonite surface temperature [oC] t time [s] V volume [m3] x, y, z cartesian co-coordinates [m] GREEK ALPHABET α heat transfer coefficient [W/m2/K] δair gap width in air-filled gap [m] δpel gap width in pellet slot [m] Δt time increment [s] ε emissivity [-] εtot total emissivity [-] φ thermal flux [W/m2] λ thermal conductivity [W/m/K] ρ rock density [kg/m3] σ Stefan-Bolzmann constant = 5.6697⋅10-8 [W/(m2K4)] SPECIAL NOTATION BWR boiling water reactor EPR European pressurized water reactor PWR pressurized water reactor VVER Russian type pressurized water reactor LO1-2 Loviisa units 1 and 2 OL1-2 Olkiluoto units 1 and 2 2D two-dimensional 3D two-dimensional ln natural logarithm

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1 INTRODUCTION The objective of this work is to evaluate the thermal behaviour of KBS-3V type reposi-tory for the fuel canisters, which are disposed at vertical position in the horizontal tun-nels in Olkiluoto. This report presents the thermal dimensioning of the repository. The design base is that the temperature at the canister/bentonite buffer interface shall not ex-ceed +100°C. The variable parameters are the distance between the tunnels and the distance between each canister in a tunnel. Figure 1 shows the principal layout of the repository. Between two panels there is a central tunnel area, on each side of which two panels are situated. In any panel the maximum length of a disposal tunnel is 350 m.

Figure 1. Principal layout of the Olkiluoto repository (Posiva Oy).

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The disposed canisters produce residual heat due to decay (or disintegration) of radio-active products inside them. The decay heat is conducted to surrounding rock mass. The thermal diffusivity of the rock is low and the heat released from the canisters is spread into the surrounding rock volume quite slowly causing thermal gradient in the rock close to canisters and the canister temperature is increased remarkably. The canister cooling condition in repository is analyzed both with the assumption of dry conditions in the disposal hole and with water saturation condition. The maximum temperature of the canister surface and the buffer takes place in about 15 years after the disposal of the canister. The dimensioning temperature of the bentonite buffer is +100°C. In the dry condition, in the dimensioning calculation, the nominal temperature is set to +95°C. The 5°C margin is showed to be enough for variation of thermal proper-ties. In normal water saturation conditions the conductivity of bentonite is much higher and the nominal maximum temperature is about +75°C. As for the temperatures, it is essential to remember that the canister is not loaded by major mechanical loads (hydro-static pressure or swelling pressure) when it is in dry conditions. In the saturated condi-tion, on the contrary pressure loads are expected. This implies that for creeping analy-ses at the canister overpack the highest reasonable temperature is about +75°C. It became apparent in the earlier analyses by Ikonen (2009) that the temperature of a canister surface can be determined by the analytic line heat source model much more efficiently than by full 3D numerical analysis. However, the analytic model needs first to be calibrated according to numerical analysis to give correct canister surface tem-perature. By superposing single line heat sources the evolution of the temperature field of the canisters and the repository can be determined efficiently. In the analytic solution the rock material must be homogeneous, it must extend to infinity and it must have con-stant diffusivity over the whole rock volume. Analytical and numerical thermal heat transfer analyses were performed with the com-puting package, which has been developed and verified at VTT. An important checking point in calculation process is the energy balance requirement: the sum of the total en-ergy penetrating the outer boundaries and the change of the enthalpy of the model should equal the energy generated inside the model.

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2 INITIAL DATA In the following, the geometry of the canisters, thermal-mechanical properties of mate-rials, decay heat correlation and emissivity of air gap surfaces are presented.

2.1 Geometry of canister near-field

Figure 2 shows the dimensions and layout of the disposal hole and tunnel for the BWR, VVER and EPR fuel canisters. The repository geometry is from Saanio et al. (2012) and the canister geometry from Raiko (2012).

Bentonite buffer

1 050

1 750

500

H2 5

00 -

2 9

00

3 500

! 4

400/ 4 0

00

Rock

Tunnel backfill

Canister

Air gap of 10 mm

Pellet slot of 50 mm

300

300

Copper plate of 30 mm

Bentonite ring of 290 mm

85

850

Figure 2. Nominal dimensions of the disposal hole and tunnel. For BWR type H = 4752 mm, for VVER type H = 3552 mm and for EPR fuel H = 5223 mm.

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All the dimensions for the fuel canisters are equal, but the canister height, which for the EPR canister is 5.223 m, for the BWR canister 4.752 m and for the VVER canister 3.552 m and the tunnel height is 4.4 m in tunnels with BWR or EPR canisters and 4.0 m in tunnels with VVER canisters. Actual tunnel dimensions may be 300-400 mm more due to over-excavation. The external diameter of the canisters is 1 050 mm. Due to manufacturing and installa-tion tolerances an annular clearance (gap) of 10 mm is assumed to exist between the canister and the buffer and an annular clearance of 50 mm between the bentonite buffer and the rock. During the first decades the inner gap on the canister surface is assumed to stay open and dry. The outer gap between the buffer and the rock is filled with bentonite pellets. In the analyses no gaps are assumed in the lower or upper end planes of the canister or the buffer due to gravity loads, which keep the interfaces closed. In the depth of 400 m the ambient rock temperature in Olkiluoto is +10.5°C and the am-bient temperature increases +1.5°C per 100 meters in downward direction. 2.2 Thermal-mechanical properties of materials

The thermal analyses are generally made with simple and theoretically well-founded methods and the thermal properties are selected to reflect the real and expected values of the properties and conditions or the parameters of the system components. Conserva-tism has been added to the allowable temperatures that are always set with a consider-able uncertainty margin. Many of the thermal analyses concerning operational phase can be verified by simple measurement during the pre-operation test phase of the encapsulation plant and reposi-tory. As for the thermal properties of large-scale rock, additional data are collected dur-ing the construction phase of the repository. Thermal dimensioning of the repository can be updated later, if new data become available and the local canister distances can be adapted accordingly even during plant operation. The thermal conductivity and the heat capacity of Olkiluoto rock are based on labora-tory measurements with core drilled samples (Kukkonen et.al 2011). The conductivity of the rock decreases slightly as a function of temperature (Figure 3a) and at the tem-peratures of 25°C, 60°C and 100°C the conductivity is 2.91±0.51, 2.82 and 2.72 W/m/K, respectively. The temperature varies in the rock around a canister be-tween 10.5…65°C. The constant average value of 2.82 W/m/K (at 60°C) is used for all the Olkiluoto repository analysis in this report in the base cases. The heat capacity of the rock increases slightly as a function of temperature and at the temperatures of 25°C, 60°C and 100°C the capacity is 712, 764 and 824±32 J/kg/K, re-spectively (Figure 3b). The value of 764 J/kg/K (at 60°C) is used throughout the analy-sis. With the rock density of 2743 kg/m3 the applied volumetric heat capacity of the rock material is 2.1 MJ/m3/K. The diffusivity d = λ /(ρc), which appears in the analytic

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formulas (Equation 8 presented later), is at the temperatures of 25°C, 60°C and 100°C 1.47.10-6, 1.34.10-6 and 1.20.10-6 m2/s, respectively.

(a) (b)

Figure 3. Conductivity and heat capacity of Olkiluoto rock (Kukkonen et al. 2011). The conductivity of bentonite buffer depends on saturation rate (Figure 4). In the nor-mal atmospheric humidity conditions the bentonite conductivity is of about 0.75 W/m/K (Börgesson 1994). In dry conditions the conductivity is about 0.3 W/m/K and in satu-rated conditions 1.3 W/m/K. In the repository condition the effective conductivity of bentonite is estimated to be 1.0 W/m/K (Hökmark et al. 2009). This estimate is based on instrumented in situ demonstration test made in Äspö.

Figure 4. Conductivity of bentonite (Börgesson 1994).

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Figure 5 shows the conductivity of air (Fletcher 1991) and humid air (relative humidity 100%) as a function of temperature. The curves are nearly same at lower temperatures. Possible humidity is diffused to bentonite. Thus the conductivity for pure air is applied. On the other hand, the possible humidity has only a minor decreasing effect on conduc-tivity. The upper curve in Figure 5a and thermal capacity in Figure 5b are approxi-mated by

!(T) = 0.0243 + 7.07"10#5 T [W/m/oC]

cv (T) = 1245 # 2.29"T [J/m3/oC]. (1) The linear fittings of Equation 1 are used in the analyses. Temperature is given in Celsius degrees. The gap between the canister and bentonite is assumed to be filled by dry air.

Figure 5. Conductivity of air (continuous line) and humid air (dotted line) in atmos-pheric pressure (a) and thermal capacity (b) (Fletcher 1991). The conductivity of a pellet slot is 0.2 W/m/K and this value is based on preliminary measurements performed at VTT in 2012. Volumetric thermal heat capacity 1.34 MJ/m3/K of the pellet slot is calculated from bentonite capacity and void fraction. Table 1 summarises thermal-mechanical properties of solid materials used in the analy-ses (Agelskog 1999, Kukkonen 2011). The tunnel backfill is of Friedland clay.

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Table 1. Thermal-mechanical properties used in the analyses.

Parameter Value Unit Reference Canister overpack conductivity 390 W/m/K Bentonite (buffer) conductivity 1.0 W/m/K Hökmark (2009) Conductivity of pellet slot 0.2 W/m/K VTT *) Volumetric capacity of pellet slot 1.34 MJ/m3/K VTT *) Rock conductivity at 60oC 2.82 W/m/K Kukkonen (2011) Tunnel (backfill) conductivity 1.6 W/m/K VTT *) Canister effective volumetric heat capacity 2.4/2.5/2.7 MJ/m3/K calculated Buffer (bentonite) volumetric capacity 2.4 MJ/m3/K Hökmark (2009) Rock volumetric capacity 2.1 MJ/m3/K Kukkonen (2011) Tunnel (backfill) capacity 1.75 MJ/m3/K VTT *)

*) Preliminary design values used at VTT. The effective volumetric thermal capacity of the whole canister, for which the values 2.4 MJ/m3/K, 2.5 MJ/m3/K and 2.7 MJ/m3/K for BWR, VVER and EPR canisters were obtained, respectively. 2.3 Emissivity of air gap surface

The radiation heat flux φrad between two flat parallel surfaces having temperatures of T1 and T2 is calculated from

!rad = "tot # (T14 $ T2

4) , (2) where the total emissivity is calculated from formula (Ryti 1973)

!tot = 1

1!1

+ 1!2

" 1 =

!1 !2

!1 + !2 " !1 !2

, (3)

where ε1 and ε2 are the emissivities of the surfaces. The Stefan-Bolzmann constant is σ = 5.6697⋅10-8 W/(m2K4). Equation 2 is applied in the narrow annular gap between the canister and bentonite. In the dimensioning case, dry condition, the most important thermal resistance for canis-ter cooling chain is the 10 mm air gap between the canister and the buffer. The thermal conduction over the gap is the sum of thermal radiation and conduction in the air. Before the maximum temperature is reached after some 15 years, the elevated temperature oxi-dizes the canister surface from the oxygen in the trapped residual air in the disposal hole and tunnel, see Performance Assessment report, section 5.1.7. The increasing oxidation makes the canister surface emissivity better and thus decreases the thermal resistance of the gap and lowers the canister temperature. When the buffer gets water, the thermal resistance is remarkably lowered and the temperature is lowered, too. The canister sur-

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face is matte after turning and somewhat oxidized during storage after encapsulation in the canister storage of the encapsulation plant or of the repository in a ventilated room for typically a few weeks. Thus the emissivity coefficient used for dry condition analy-ses, 0.3, is conservative at least for longer term and in particular, when the maximum temperature is expected after 10 to 15 years. The emissivity of the copper surface depends strongly on the quality of the surface. Polished surface has an emissivity of about 0.02, clean machined surface about 0.3 and oxidised surface 0.6 Ryti (1973). In the analyses the emissivity of the copper surface is assumed to be 0.3. Total emissivity expressed by Equation 3 is applied in a narrow cylindrical gap between the canister and bentonite (view factor = 1). If the gap width increases, view factor is less than one and total emissivity is calculated from Mills (1999)

!tot = 1

1 " !1!1

+ 1

F12

+ 1 " !2!2 (r2/r1)

, (4)

where r1 and r2 are the radii of the internal and external cylinders and view factor F12 = 1 (other view factors between internal and external cylinders 1 and 2 are F11= 0, F21 = r1/r2 and F12 = 1 - F21). If for instance r1 = 0.525 m, gap width is 10 mm, i.e. r2 = 0.535 m, ε1 = 0.3 and ε2 = 0.8, it follows from Equation 4 that εtot = 0.2794. From Equation 3 follows εtot = 0.2791. If the gap width is 50 mm, from Equation 4 follows εtot = 0.2808. Thus Equation 3 gives accurate enough results in case of gap widths in practise. 2.4 Exponential decay heat modelling

The decay heat decreases strongly with time and, for example, after 50 years the decay heat is only a half of the amount it was during disposal. The decay power of the spent fuel was calculated by Anttila (2005) with the ORIGEN-S computer code of the TRITON functional module of the SCALE program package (Oak Ridge National Laboratory 2004). Reasonable decay heat level is reached in 30 to 50 years cooling time depending on burn-up value of the spent fuel. Figure 6 shows decay power of spent fuel according to ORIGEN-S calculations Anttila (2005). Numerical values of the decay power are shown in Table 2. The average burnup of all spent fuel for Olkiluoto 1 and 2 (OL1, OL2) as well as Lovi-isa 1 and 2 (LO1, LO2) units is about 40 MWd/kgU and the estimated average burnup from Olkiluoto 3 and 4 (OL3, OL4) units will be about 45 MWd/kgU. Thus the decay power functions have been selected as 40 MWd/kgU for OL1&2 and LO1&2 canisters and conservatively 50 MWd/kgU for OL3&4 canisters.

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Figure 6. Decay heat densities of BWR, VVER and EPR fuels as a function of cooling time in years. Decay power between two calculated points is interpolated by a linear fitting on log-log-coordinate system

ln P = a + b ln t . (5)

By setting the times of the end points t1 and t2 and corresponding powers P1 and P2 the coefficients a and b of the fitting are solved and the interpolation for the power is

ln P

P1

=

ln P1

P2

ln t1

t2

ln t

t1

.

(6)

This fitting is accurate enough, if the points are given after sufficiently short time in-crements, for instance after every 10 years.

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Table 2. Decay heat of BWR, VVER and EPR spent fuel (Anttila 2005).

Decay heat [W/tU] Time [years]

BWR 40 MWd/kgU

VVER 40 MWd/kgU

EPR 50 MWd/kgU

10 1339.0 1416.0 1890.0 20 1036.0 1107.0 1455.0 30 854.4 927.5 1204.0 40 713.8 787.6 1013.0 50 602.7 675.9 862.9 60 514.0 586.6 743.9 70 443.0 514.6 648.8 80 386.1 456.5 572.5 90 340.1 409.2 510.9 100 303.1 370.9 460.8 110 273.1 339.5 419.9 120 248.5 313.6 386.3 130 228.5 292.2 358.4 140 211.8 274.3 335.1 150 198.0 259.2 315.4 160 186.6 246.5 298.5 170 176.8 235.5 284.2 180 168.5 226.1 271.7 200 155.2 210.5 251.2 300 119.5 165.6 191.9 600 77.8 107.0 120.2 1000 51.8 69.5 77.6 3000 22.3 27.7 30.5 6000 17.1 21.3 23.3 10000 13.1 16.8 18.0 30000 4.9 6.8 6.9 60000 2.2 2.9 3.0 100000 1.1 1.4 1.5 300000 0.6 0.7 0.9

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3 CALCULATION METHODOLOGY Calculation methodology combines analytical and numerical methods. Analytical ap-proach is much more efficient than numerical approach, but canister surface tempera-ture calculation by analytic method needs first calibration by numerical analysis. Heat transfer across the air-filled gap will take place by conduction, radiation and con-vection. The effect of convection is conservatively neglected, since the gaps are rather small and the surfaces are rough. Heat transfer across the outer gap of 50 mm filled with bentonite pellets will take place by conduction and to some extent by convection. The surfaces of bentonite and rock are rough. The effect of convection in the gap is as-sumed to be small and it is conservatively neglected in the gap heat transfer modelling.

3.1 Analytical solution

The starting point for the analytic solution is a case, where an energy of Q is instantane-ously released at a certain point in spherical symmetry. In this case the solution for a point heat source in an infinite space the temperature in a considered point is

T(r, t) = Q

! c (4 " d t) 3/2 e# r2

4 d t .

(7)

where d = λ /(ρc) is thermal diffusivity of the material (λ , ρ and c are thermal conduc-tivity, density and thermal capacity of the material, respectively, and they are constants in the whole space), r is distance and t is time. This solution can be extended to a line heat source case. In an xyz co-ordinate system the temperature in a considered point and caused by a line heat source (Figure 7) aligned vertically with z axis is

T(x, y, z, tmax) = 1/H! c 4" d

0

tmaxP(t)

tmax # t e

# x2 + y2

4 d (tmax # t)

’ 12

{erf [ 1

2 d (tmax # t) ( H

2 + z)] + erf [ 1

2 d (tmax # t) ( H

2 # z)]} dt ,

(8)

where H is the height of the vertical line heat source, P is the time dependent power and tmax is the considered time dt is the time differential.

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z

r xy

x, y, z

Considered point

H

Figure 7. Line heat source. In practice, temperature T(x, y, z, tmax) from Equation 8 is calculated by numerical in-tegration. If low conductivity or high capacity is used, the temperature will be conser-vatively overestimated. The flow of the groundwater and the small heat flow caused by this is conservatively not taken into account. The assumptions concerning Equation 8 are that the material (now rock) is homogene-ous, it extends to infinity, has constant thermal diffusivity and the line heat source has uniform power generation. Equation 8 can be applied in the whole infinite rock for an actual spent fuel canister except in the very near surrounding area of the canister. The accuracy of Equation 8 is improved, if the height H of the canister is replaced by the effective height Heff as presented later. 3.2 Effective height of the canister Equation 8 can be applied for calculating the temperatures of the surrounding of the cy-lindrical canister with reasonable precision, when the actual height of the canister is re-placed by the effective height. In the mid-height of the canister the temperature gradi-ent in vertical direction equals zero from symmetry reasons and the highest tempera-tures are practically induced in the mid-height also in the buffer and rock.

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r /2

r /20

H H + r

2 r

0

0

0

Figure 8. Effective height of the canister. Let us set a requirement that on the mid-height of the canister heat is transferred in line source model equal to

qmean = !mean 2" r0 ,

(9)

where qmean is the line density of heat power in the line model and φmean is the mean heat flux through the whole external surface of the canister. The mean heat flux φmean is obtained by dividing the power P by the total area of the canister giving

!mean = P

2"r0H + 2"r02 =

P

2"r0 (H + r0) . (10)

Equations (9) and (10) give the mean line heat density

qmean = PH + r0

. (11)

The effective height Heff in the line heat source model (8) is then (Figure 8)

Heff = H + r0 . (12) Equal effective height result can be obtained also geometrically by extending the cylin-der so that the area of the extension of the cylinder equals the areas of the circular lids. The actual height of the canister is substituted by this height.

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3.3 Evaluation of canister surface temperature in analytic line heat source analysis

The highest temperature on the canister surface, which is the most important dimen-sioning quantity, is calculated in the mid-height of the canister with the applied bound-ary conditions. When applying the line heat source solution 8 the temperature of the canister surface needs to be evaluated in a special way. In the following a formula for calculating the canister surface temperature T0 is presented, when the rock wall tem-perature Trock is determined by the line model from Equation 8 and the mean heat flux φmean given by Equation 11 is reduced to give the heat flux φ0 in the mid-height of the canister in a way as presented later. In the axisymmetric model the clearances are assumed to be of uniform width around the entire circumference. The average dimensions of the gap are used. Heat transfer across the air-filled gap will take place by conduction, radiation and convection. The effect of convection is conservatively neglected, since the gap width is only 10 mm and the surface of bentonite is rough.

r0

T

r

rrock

Rock

Bentonite

Canister

T

0b

0

Trock

Air gap of 10 mm

Pellet slot of 50 mm

Figure 9. Air- and pellet-filled gaps on canister surface cylinder and between buffer and rock.

17

On the mid-height of the canister and close to the canister surface the temperature field is cylindrically symmetric, whereas in greater distances the temperature field becomes spherically symmetric (see e.g. later Figure 9b in the Appendix, based on numerical analysis, different height of the buffer above and below the canister and the different conductivity of the tunnel backfill material have no visible effect). Due to cylindrical symmetry the vertical thermal gradient equals zero in the mid-height and heat flow in vertical direction is accordingly zero. The situation can be considered as heat conduction in the horizontal insulated plate. Temperature T0b on the external surface of the air gap (i.e. on the internal surface of the bentonite, Figure 9) is calculated by adding the temperature increments formed on the pellet slot and bentonite layers to the temperature Trock on the disposal hole (rock wall)

Tbentonite surface = Trock wall + !Tpellet slot + !Tben

= Trock wall + "0 r0

#w ln

rrock

rrock $ %pel + "0 r0

#ben ln

rrock $ %pel

r0 + %air ,

(13)

where δair and δpel are the widths of the air and pellet gaps. Due to continuity of heat flux over the air gap it can be written (see Equation 4)

!0 = "air T0 # T0b

r0 ln (1 + $air/r0) +

% (T04 # T0b

4 )

1 # &1&1

+ 1F12

+ 1 # &2&2 (r2/r1)

= ["air $air

r0 ln (1 + $air/r0) + $air &tot % (T0 + T0b) (T0

2 + T0b

2 )] T0 # T0b

$air

.

(14)

Total emissivity is calculated in case of wide gap from Equation 4 and in case of thin gap from Equation 3. In the last term related to radiation the temperatures are expressed in Kelvin scale. Radiative heat transfer can be expressed as effective heat conductivity

!eff = "air #tot $ (T0 + T0b) (T02 + T0b

2 ) ! 4 "air #tot $ Tmean3 ,

(15)

where Tmean is the mean temperature in the gap (the average of the surface tempera-tures). If the width of the air gap is, for instance 10 mm, the mean temperature 80°C and total emissivity 0.5, the effective conductivity is λeff = 0.050 W/m/K. The conduc-tivity of air at 80°C is 0.030 W/m/K when calculated from Equation 1. Effective con-ductivity decreases proportionally to the air gap width δair. In the numerical heat con-duction analysis the radiative heat transfer term in Equation 14 can be substituted by ef-fective conductivity of Equation 15.

18

The equation for solving the canister surface temperature T0 starting from the rock sur-face temperature Trock is

T0 = Trock + !0 [r0

"w ln

rrock

rrock # $pel +

r0

"ben ln

rrock # $pel

r0 + $air

+ 1"air

r0 ln (1 + $air/r0) + %tot & (T0 + T0b) (T0

2 + T0b2 )

] .

(16)

Last row is related to the air gap. Inaccuracies are primarily related to the rock surface temperature Trock and the thermal flux φ0 in the mid-height of the canister (in boxes). The rock wall temperature Trock and the heat flux φ0 in the middle of the canister sur-face may be inaccurate, since the radius of the heat source (canister) does not equal to zero as assumed in the line heat model (8), the system consists of different materials and there are internal gaps. Further, the temperature field is not in steady state. However, the transient is so slow that assumption of steady state is valid. The inaccuracy is pri-marily related to the thermal flux φ0, which is corrected as follows. The reduction of thermal flux φ0 in the mid-height of the canister can be presented by introducing the heat flux reduction coefficient k (Equation 10)

!0 = k !mean = k P

2"r0 (H + r0) . (17)

Equation 16, i.e. the iteration formula of the canister surface temperature T0 can finally be written as

T0 = Trock + k !mean [r0

"w ln

rrock

rrock # $pel +

r0

"ben ln

rrock # $pel

r0 + $air

+ 1"air

r0 ln (1 + $air/r0) + %tot & (T0 + T0b) (T0

2 + T0b2 )

] .

(18)

Since the rock wall surface temperature of the hole Trock is obtained with the assump-tion of the line heat source sufficiently accurately and this temperature is not the design basis temperature like canister surface temperature, the only quantity requiring numeri-cal analysis is the heat flux reduction coefficient k (≈ 0.8, for ideal line heat source k = 1), which is calibrated according to the numerical analysis as presented in the Appendix.

19

3.4 Numerical solution

The objective of numerical heat conduction analysis is to calibrate the analytical line heat source model when using it for calculating the canister maximum surface tem-perature, which is the most important output quantity. The canister is assumed to be homogeneous with uniform power generation over its volume inside the 50 mm thick copper overpack and the heating input in the insert is not modelled in detail, since the copper overpack has very high thermal conductivity (390 W/m/K) causing practically uniform temperature distribution on the external surface of the canister. Temperatures inside the canister were analyzed in detail in Ikonen (2006). In this context it is important that the modelling of the canister is thermally equivalent in the simplified modelling and in the actual case. Essential parameters are the total the decay power and the effective volumetric thermal capacity of the entire canister. For handling the temperatures on the outer edges of the numerical model two alterna-tives exist. The edges may be chosen far from the canister to avoid heat pulse reflection from the edge. This makes the model large. The other possibility is to calculate the temperatures on the boundaries from the analytic solution (Equation 8). The latter al-ternative is adopted.

20

21

4 ANALYSIS OF CANISTER PANEL In the following a BWR, VVER and EPR canister panel of the repository residing in different depths between 400 m and 450 m is analyzed. Table 3 presents the common initial values for the analysis. It is assumed that at disposal the pre-cooling time and the initial decay heat is the same for all the canisters. Calculation panel is assumed to be a very large rectangular area of rock, where canisters are located evenly distributed. The panel is so large that the central area is practically not affected by the boundaries. In long term, heat is removed from the canisters on the central area mainly in vertical di-rection upwards and downwards. Table 3. Initial common values of fuel repository and rock (values concern also the base case defined in Chapter 4.1, when tunnel spacing is 25 m).

Tunnel spacing 25/30/40 m Number of canisters in a tunnel 30 - Number of tunnels in a repository panel 30 - Number of canisters in a panel 900 - Ambient rock temperature (-400 m) +10.5 °C Rock conductivity 2.82 W/m/K Rock volumetric heat capacity 2.10 MJ/m3/K Canister external diameter 1 050 mm Rock wall diameter of the disposal hole 1 750 mm Bentonite conductivity (initial) 1.0 W/m/K Bentonite conductivity (saturated) 1.3 W/m/K Width of air gap on copper cylinder 10 mm Width of pellet slot 50 mm Pellet slot conductivity 0.2 W/m/K Volumetric capacity of pellet slot 1.34 MJ/m3/K Emissivity of copper surface 0.30 - Emissivity of bentonite surface 0.80 - Total emissivity of the air gap 0.279 -

The analyses are performed by applying the analytic line heat source model (8) and su-perposing the effect of all canisters yielding the rock wall temperature Trock in Equation 18 near the considered canister. The effective height Heff = H + ro (Equation 12) is used instead of the actual height of a canister. The mean heat flux φmean is calculated from Equation 10. The value of the heat flux reduction coefficient k was determined, as demonstrated for BWR canister in the Appendix, by calibrating the analytical solution to obtain correct canister surface temperature in the mid-height of the canister. Coeffi-cient values kBWR = 0.829, kVVER = 0.811 and kEPR = 0.833 were obtained in dry case by applying the control volume meshes, which were three times denser than the basic

22

mesh. The time step is 600 s and the balance iteration at every time increment is stopped, when temperature change becomes less than 0.001oC. The heat flux reduction coefficient is determined in the Appendix with a single canister and assuming the ambient rock temperature 10.5°C. Due to interaction of many canis-ters the temperature of the surrounding rock increases in real multiple canister case for instance, for a BWR canister by about 12°C (= 95°-83°). Consequently the radiative heat transfer is increased in the air gap and further the heat flux reduction coefficient is increased. This would decrease the needed canister spacing by about 4 cm. The effect is thus small and can be ignored. There are totally 900 canisters in one calculation panel. It takes 25/25/18 years to dis-pose all BWR/VVER/EPR canisters into one panel, when the disposing rate is 36/36/50 canisters per year. The varied distance between tunnels is 25 m, 30 m or 40 m. Table 4 presents the initial fuel data. Decay heat rate of different fuels are presented in Chapter 2.4. Table 4. Initial data of different fuel types.

Canister type BWR VVER EPR Average burn-up value [MWd/kgU] 40 40 50 Pre-cooling time [years] 32.95 28.30 50.26 Decay heat power at disposal [W/canister] 1700 1370 1830 Amount of uranium in a canister [tU] 2.11 1.44 2.13 Canister height [m] 4.752 3.552 5.223 Disposal rate [canisters per year] 36 36 50 Heat flux reduction coefficient k [-] x 0.829 0.811 0.833

In the air gap the conductivity and the capacity of air are calculated from the fittings (1). The heat flux reduction coefficients k was determined with three times denser mesh than for the basic mesh. 4.1 Definition of base case

Because there are three different fuel types under different conditions and some more detailed analyses are not needed to be performed for all the fuel types, it is practical to define a base case. Base case is defined to be formed of the BWR fuel canister. The dimensions are presented in Figure 2, thermal-mechanical properties in Table 1, decay heat is presented in Table 2 and more data related for it is presented in Table 3. The heat flux reduction coefficient k for BWR fuel is determined to be kBWR = 0.829 (see the Ap-pendix). The corresponding base case panel consists of 30x30 = 900 canisters. The tunnel spacing is 25 m and the canister spacing 8.92 m (determined in Chapter 4.2, see Table 11).

23

4.2 Dependence of maximum canister surface temperature on canister spacing

Figure 10a demonstrates the disposing order of BWR canisters in a panel in the base case.

(a)

(b)

Figure 10. Temperature distribution in the base case (dry) after 24 years operation, when the highest temperature 95°C is reached on the hottest BWR canister surface. Canister spacing is 8.92 m and tunnel spacing 25 m. On the white isotherm the tem-perature is 11.0°C (10.9°C-11.1°C) and on the pink isotherm 15.0°C (14.5°C-15.5°C), respectively.

24

Figure 10 demonstrates further the temperature distribution after 24 years of operation, when the highest temperature 95°C is reached. Canister spacing 9.82 m is determined in Chapter 4.3. In Figure 10b, asymmetry in vertical direction is caused by the initial undisturbed temperature gradient in vertical direction. Due to low conductivity of the rock the heated area spreads rather slowly. During the first 200 years the thermal im-pulse has not yet reached the ground surface. For rock mechanical reasons the distance between disposal holes shall not be less than 6 m. 4.2.1 BWR fuel canisters in dry case

Here the dry case mean the situation, where the gap of 10 mm between the canister and the buffer is filled by air and the gap of 50 mm between the buffer and the rock is filled with dry pellets. Table 5 and Figure 11 show the maximum canister surface tempera-ture as a function of spacing between the BWR canisters when the tunnel spacing is 25 m (the base case), 30 m or 40 m. With very large canister spacing the maximum canis-ter surface temperature decreases to about 83°C without the heating effect of the neigh-bouring tunnels (see Figure 10 in the Appendix concerning a single canister). Table 5. Maximum BWR canister temperatures in dry case (base case, when tunnel spacing is 25 m).

Canister spacing [m]

Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

4 (115.8) 5 (114.2) (107.3) 6 110.9 105.2 100.3 7 103.5 99.0 95.6 8 98.5 94.9 92.4 9 94.7 92.2 90.1 10 92.1 90.1 88.5 11 90.3 88.6 87.4 12 88.9 87.3 86.5 13 87.7 86.4 85.8 15 86.0 85.2 84.8 17 85.1 84.5 84.3 20 84.2 84.0 83.9

25

Due to gravity the canister is always in a contact with buffer at some places. Since the conductivity of copper is very high (390 W/m/K), the temperature on the surface of the canister is practically constant. Thus the maximum temperature of the buffer equals to the surface temperature of the canister. The surfaces temperatures of the canister illus-trated in Figure 11 are directly applicable temperature estimates also for the buffer.

Figure 11. Maximum BWR canister surface temperature vs. canister spacing in dry case when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 40 MWd/kgU. Initial canister power is 1700 W. Numerical values are shown in Table 5. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 5oC (= 100°C-95°C).

26

4.2.2 VVER 440 fuel canisters in dry case

Table 6 and Figure 12 show the maximum canister surface temperature as a function of VVER canister spacing with the tunnel spacing being 25 m, 30 m or 40 m. Table 6. Maximum VVER canister temperatures in dry case.


Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

5 (111.1) (105.6) (100.6) 6 102.7 98.5 94.9 7 97.0 93.7 91.1 8 93.1 90.4 88.8 9 90.2 88.3 87.2 10 88.2 86.7 86.0 11 86.7 85.7 85.1 12 85.6 84.9 84.5 13 84.9 84.3 84.1 14 84.3 83.9 83.7 15 83.9 83.6 83.5 16 83.4 83.4 83.6 17 83.3 83.2 83.1 18 83.2 83.0 82.9 19 83.0 82.9 82.8 20 83.0 82.8 82.7

27

Figure 12. Maximum VVER canister surface temperature vs. canister spacing in dry case, when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 40 MWd/kgU. Initial canister power is 1370 W. Numerical values are shown in Table 6. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 5oC (= 100°C-95°C).

28

4.2.3 EPR fuel canisters in dry case

Table 7 and Figure 13 show the maximum canister surface temperature as a function of EPR canister spacing with the tunnel spacing being 25 m, 30 m or 40 m. Table 7. Maximum EPR canister temperatures in dry case.


Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

6 112.2 104.8 7 111.2 104.8 99.1 8 104.7 99.5 95.2 9 99.9 95.8 92.5 10 96.4 93.1 90.5 11 93.8 91.0 89.0 12 91.8 89.5 87.9 13 90.2 88.4 87.2 14 89.0 87.4 86.6 15 88.1 86.7 86.0 16 87.3 86.2 85.6 17 86.6 85.8 85.3 18 86.1 85.4 85.0 19 85.7 85.2 84.9 20 85.5 84.9 84.7

29

Figure 13. Maximum EPR canister surface temperature vs. canister spacing in dry case, when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 50 MWd/kgU. Initial canister power is 1830 W. Numerical values are shown in Table 7. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 5oC(= 100°C-95°C). After the temperature value of 95°C the gradients of the curves for BWR, VVER and EPR canisters are 2.5°C/m, 3.5oC/m and 5.1°C/m. The results for the EPR canister in-dicate higher sensitively of canister to the heating power (Figure 20). The thermal power of EPR fuel assemblies packed in a canister is 1830 W. If all the canisters would be disposed simultaneously, the results in Figures 11-13 would change a very little. Simultaneous disposal of 900 canisters causes about 0.3°C higher maximum temperature than the actual disposal rates of 36, 36 or 50 canisters per year for BWR, VVER and EPR fuel disposal canisters, respectively, during 18-25 years. Thus the higher disposing rate has an insignificant effect on the maximum canister sur-face temperature.

30

4.2.4 BWR fuel canisters in saturated case

Here the saturated case means the situation where no gap between the canister and the buffer exists and the gap of 50 mm between the buffer and the rock is filled by water and pellets. Thermal conductivity of the pellet-filled slot is assumed to be 0.6 W/m/K in saturated case (greater values do not change the results as can be seen from Figure 29 later). The buffer is also supposed to be water saturated and the conductivity is 1.3 W/m/K. Table 8 and Figure 14 show the maximum canister surface temperature as a function of BWR canister spacing, when the tunnel spacing is 25 m, 30 m or 40 m. Table 8. Maximum BWR canister temperatures in saturated case.


Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

5 105.7 (97.0) (88.1) 6 94.6 87.2 80.0 7 86.4 80.2 74.3 8 80.3 75.1 70.3 9 75.6 71.4 67.6 10 72.2 68.6 65.6 11 69.5 66.4 64.0 12 67.4 64.7 62.8 13 65.7 63.5 61.9 14 64.3 62.5 61.1 15 63.2 61.8 60.5 16 62.5 61.1 60.1 17 61.8 60.6 59.7 18 61.2 60.1 59.4 19 60.8 59.7 59.2 20 60.4 59.4 58.9

31

Figure 14. Maximum BWR canister surface temperature vs. canister spacing in satu-rated case, when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 40 MWd/kgU. Initial canister power is 1700 W. Numerical values are shown in Table 8. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 10oC (= 100°C-90°C).

32

4.2.5 VVER 440 fuel canisters in saturated case

Table 9 and Figure 15 show the maximum canister surface temperature as a function of VVER canister spacing, when the tunnel spacing is 25 m, 30 m or 40 m. Table 9. Maximum VVER canister temperatures in saturated case.


Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

5 (94.5) (87.7) (80.5) 6 85.3 79.5 73.9 7 78.6 73.6 69.4 8 73.7 69.7 66.2 9 69.9 66.8 64.0 10 67.3 64.6 62.4 11 65.2 63.0 61.1 12 63.6 61.6 60.3 13 62.3 60.7 59.7 14 61.3 59.9 59.2 15 60.4 59.3 58.7 16 59.8 58.8 58.4 17 59.3 58.5 58.1 18 58.9 58.3 57.9 19 58.5 58.0 57.8 20 58.3 57.8 57.7

33

Figure 15. Maximum VVER canister surface temperature vs. canister spacing in satu-rated case, when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 40 MWd/kgU. Initial canister power is 1370 W. Numerical values are shown in Table 9. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 10oC (= 100°C-90°C).

34

4.2.6 EPR fuel canisters in saturated case

Table 10 and Figure 16 show the maximum canister surface temperature as a function of EPR canister spacing, when the tunnel spacing is 25 m, 30 m or 40 m. Table 10. Maximum EPR canister temperatures in saturated case.


Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m


Tmax [°C]

Tmax [°C]

Tmax [°C]

6 104.9 95.7 95.2 7 95.5 87.5 85.8 8 88.1 81.4 79.2 9 82.6 76.7 74.4 10 78.2 73.0 70.9 11 74.7 70.3 68.3 12 71.9 68.1 66.3 13 69.6 66.4 64.8 14 67.9 65.0 63.7 15 66.4 63.9 62.8 16 65.3 63.0 62.0 17 64.3 62.3 61.4 18 63.4 61.7 60.9 19 62.7 61.3 60.5 20 62.1 60.9 60.2

35

Figure 16. Maximum EPR canister surface temperature vs. canister spacing, when tunnel spacing is 25 m, 30 m and 40 m and burn-up value is 50 MWd/kgU. Initial can-ister power is 1830 W. Numerical values are shown in Table 10. Initial values are listed in Tables 3 and 4. Inaccuracy margin is 10oC (= 100°C-90°C). The analyzed dry and saturated cases show that the saturated case gives always signifi-cantly shorter canister spacing (about 2 m shorter) with same maximum temperature. 4.3 Canister spacing causing maximum allowable canister temperature Canister spacings are solved by iteration so that maximum canister surface temperature is restricted to 95°C in dry condition and to 90°C in saturated, whichever is more re-strictive. Table 11 shows the result for BWR, VVER 440 and EPR canisters.

36

Table 11. Canister spacing for BWR, VVER 440 and EPR canisters in dry case. Initial values are listed in Tables 3 and 4.

Canister type BWR VVER EPR Tunnel spacing 25 m

Canister spacing [m] causing T = 95°C 8.92 7.48 10.51 Canister spacing in simultaneous disposal [m] 9.05 7.58 10.66 Tunnel spacing 30 m


Canister spacing [m] causing T = 95°C 7.17 5.97 8.05 Canister spacing in simultaneous disposal [m] 7.21 6.00 8.15

Table 12 shows the result for BWR, VVER 440 and EPR canisters in saturated case, when the maximum canister surface temperature is restricted to 90°C. Table 12. Canister spacing for BWR, VVER 440 and EPR canisters in saturated case. Initial values are listed in Tables 3 and 4.

Canister type BWR VVER EPR Tunnel spacing 25 m



Canister spacing [m] causing T = 90°C 4.82 4.07 5.51 Canister spacing in simultaneous disposal [m] 4.84 4.09 5.54

Simultaneous disposal of all canisters in the whole panel would increase the canister spacing by 6-11 cm when compared to the canister spacing obtained by the actual dis-posal ratio. Figure 17 shows the temperature distributions after 25 years, when the disposal rate is 36 canisters per year and the tunnel spacing is 25 m or 40 m.

37

(a) (b) Figure 17. Temperature distribution of a panel after 25 years operation, when the dis-posal operation for this panel has been finished. BWR canister power 1700 W, canister spacing 8.92 m and tunnel spacing 25 m (a, the base case) and canister spacing 7.17 m and tunnel spacing 40 m (b). On the white isotherm the temperature is 11.0°C (10.9°C-11.1°C) and on the pink isotherm 15.0°C (14.5°C-15.5°C), respectively. Figure 18 shows the corresponding temperature distributions, if all the canisters are fic-tively disposed simultaneously.

38

(a) (b) Figure 18. Temperature distribution of a panel after 25 years, when all canisters are fictively disposed simultaneously. BWR canister power 1700 W, canister spacing 9.05 m and tunnel spacing 25 m (a) and canister spacing 7.21 m and tunnel spacing 40 m (b). On the white isotherm the temperature is 11.0°C (10.9°C-11.1°C) and on the pink isotherm 15.0°C (14.5°C-15.5°C), respectively.

39

Figure 19. Maximum temperature envelope on any BWR canister surface in base case. Canister spacing is 8.92 m and tunnel spacing 25 m. Panel size 30x30. Figure 19 presents the maximum temperature evolution on all BWR canister surfaces, when the canister spacing is 8.92 m when assuming the actual disposal rate, and 9.05 m when assuming fictive simultaneous disposal. At the actual disposal rate the maximum allowable surface temperature 95°C is achieved after 15 years from the beginning of the disposal and after about 35 years the maximum temperature begins to decrease slowly.

Figure 20. Minimum canister spacing as a function of decay heat at disposal. Points for EPR 1900 W and EPR 2000 W are fictive. Figure 20 presents the minimum canister spacing for BWR, VVER and EPR canisters as a function of decay heat load at the disposal. The cases with decay power being

40

1900 W and 2000 W in EPR canisters are fictive and they suggest that the needed can-ister space and also cost would to increase strongly, if the decay heat per canister be-came greater than about 1800 W. 4.4 Effect of various saturation degrees of bentonite buffer During the first decades the inner gap on the canister surface is assumed to stay dry. The outer gap between the buffer and the rock is assumed to be pellet-filled. Red line in Figures 21-23 shows evolution of the maximum canister temperature in the repository in dry case, when the air gap is conservatively assumed to be open during whole analy-sis. The outer gap between the buffer and the rock is assumed to be pellet-filled. Later, after the disposal, air gaps are closed due to saturation and swelling of bentonite. Green line shows the saturated buffer case, where the bentonite thermal conductivity is 1.3 W/m/K and the gap is closed. The black line shows the temperature on the rock edge of the disposal hole. Thermal conductivity of the pellet-filled slot is 0.2 W/m/K in dry case and 0.6 W/m/K in saturated case (greater values do not change the results as can be seen from Figure 30). In practice, the actual maximum canister surface tem-perature will always be between these two extremes 95°C and 76°C. The tunnel spac-ing is 25 m.

Figure 21. Temperatures in the marked places of a BWR canister locating centrally in a panel in dry case (red line) and in saturated case (green line). Black line shows rock surface temperature in both cases. Canister spacing is 8.92 m (from Table 11).

41



42

4.5 Effect of changing canister distance on edge areas In the previous analyses the canister spacing was kept constant in the panel. However, the temperature of the canisters is lower on the edge areas of the panel than in the mid-dle area. Thus it is possible to pack the canisters denser on the edge areas to lower the costs. This topic has been studied in Ikonen (2009). The total saving in the needed lengths of the tunnel for 900 canisters in one panel would be hundreds of meters. This corresponds up to 5 % relative saving depending on the fuel type and tunnel spacing. 4.6 Temperature interaction between panels For studying interaction between side-by-side panels, external temperatures of one panel at different times in the base case (defined in Chapter 4.1) are determined in the next. Figures 24-27 show the results. Superposition principle can be applied to deter-mine the interaction of two panels. All the basic thermal dimensioning before was made taking into account the interaction of the canisters in the calculation panel only. The calculation panel is so large that the maximum temperature is insensitive to small variations in the panel size. The disposal rate is assumed to be 36-50 canisters per year. A higher rate does not have a significant effect on the maximum temperature. The calculation was made even for extreme situa-tion, where all the canisters of a panel are disposed at the same time. The maximum temperature in the canister will be almost the same as for the base case. The interaction of separate panels becomes remarkable and harmful, if the time delay before the neighbouring panels are started to be taken into use becomes long, i.e. tens of years. In the following, the calculated temperature fields around a single panel are given in Figures 24 to 27. These graphs tell how much the rock temperature is increasing in each four directions around a rectangular panel after the disposal of the canisters in the panel. The time starts to run from the first disposal of a canister in the panel in ques-tion. The initial temperature of the rock to be used for disposal should not increase more than 1 to 2°C before starting the operation. If the initial temperature is increased more, the change should be taken into account in adjusting the canister distances in the panel that is disposed later, in other words, the canister distances should be increased so that the maximum temperature will stay within the limits. The distance between panels is calculated from the outermost canister locations in the neighboring panels. Using the graphs in Figure 27 we can make a check on how much later a panel of canisters can be disposed on the opposite side of the central tunnel area. The closest distance of the outermost canisters in neighboring panels on opposite sides of the central tunnel area is about 88 m. The graphs in Figure 27 show that if the dis-tance between the nearest canisters is 88 m, the time delay between the canister disposal into the second panel can be 40 to 60 years later without excessive thermal interaction. The disadvantageous thermal interaction may appear also in cases when second panel is started remarkably later as a continuation to the earlier first panel. Also then, possible

43

additional distance is needed to avoid excessive thermal interaction. The graphs in Fig-ures 24 to 27 give tools to make the thermal interaction check on all four side of a panel.

Figure 24. Rock temperature distributions from the lowest canister row outwards from the start side of the repository panel and on the middle of the side. BWR canisters in the base case, 8.92 m canister distance and 25 m tunnel distance.

44

Figure 25. Rock temperature distributions from the end side outwards from the end side of the of repository panel and on the middle of the side.

Figure 26. Rock temperature distributions outwards from the tunnel end side of re-pository panel and on the middle of the side.

45

Figure 27. Rock temperature distributions outwards from the central tunnel side of re-pository panel and on the middle of the side. 4.7 Effect of inaccuracy of canister position In drilling the hole for a canister there may be a need to change slightly its location due to local rock quality. Figure 28 shows, how the maximum canister surface temperature is increased as a function location inaccuracy. Generally, the rock temperature is quite evenly distributed in a panel and the level of temperature is dependent on the decay power density in the panel area, for example in units W/m2. A sensitivity calculation was made in a way that first a whole panel was modelled with nominal canister locations and then, in a tunnel in central area of panel, the locations of all canisters were relocated with a constant amount as follows: Half of the canister in one half of the tunnel locations were shifted a constant amount towards the centre of the tunnel length and the other half of the locations were shifted to the other direction. This configuration gives the highest increase to the canister temperature in the centre of the tunnel and in the centre of the panel. The calculation model can also be described in another way. All the other canister dis-tances from each other are nominal, but the distance between the two most central canis-ters is shortened with two times the allowable inaccuracy length. An example, if the in-accuracy in each canisters position is +/-0.5 m the distance between the two central canisters is shortened with 2*0.5 m = 1.0 m. And all the other canisters in the tunnel are shifted 0.5 m towards the central canisters. This configuration cumulates the highest

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decay power concentration around the central canisters and gives the maximum tempera-ture increase response for dimensioning purposes. The effect from the inaccuracies of the other tunnel on local temperature does not have any local effect in the distance of 25 m or more from the target of this inaccuracy analy-sis. The result of the inaccuracy analysis is, according to Figure 28, as follows. If we allow the canister maximum temperature increase of +1°C locally, then the rule is as follows. The inaccuracy of +/-0.5 m in any canister location from the nominal position is allow-able in all canister positions of the whole panel. This rule can be defined also in another way. If the position of any canister in the rest of the tunnel must be shifted more than +0.5 m from nominal, then the rest of canister positions shall be shifted accordingly.

Figure 28. Effect of inaccuracy of canister position in the tunnel on maximum canister surface temperature. 4.8 Quality control of the analyzing process 4.8.1 Applied means for quality control

The following points can be listed in assessing the reliability of the computing process: • Comparison of the results obtained with the control volume program and with some

known analytic solutions has been done and the results are equal with high accuracy.

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• The control volume program and the analytic line solution in case of one canister give equal results far from the canister in the test cases.

• Energy balance is checked after every time step meaning that the energy fed to the model must equal to the change of the enthalpy plus the energy escaping through the boundaries.

• Doubling the mesh density in the control volume program give closely equal results with the coarser grid. This result eliminates a great number of possible errors and in-accuracies.

• Comparison with SKB analyses (Hökmark et al. 2009) in one case (presented in Chapter 4.7.1) gives a similar result for the BWR canister distances. The SKB analysis system is independent of the analysis system used in this study.

4.8.2 Comparison to SKB analyses

In the following a BWR canister panel of the repository is analyzed trying to use, as far as possible, the same initial data as SKB analyses (Hökmark et al. 2009). It is assumed that in the disposal the pre-cooling time and the initial decay heat values of Table 2 for BWR fuel are the same for all the canisters. Tables 13 and 14 present the initial data for the comparison analysis. Table 13. Initial values for simulating SKB fuel repository and rock.

Tunnel spacing 40 m Number of canisters in a tunnel 30 - Number of tunnels in a repository panel 30 - Number of canisters in a panel 900 - Ambient rock temperature 11.0 °C Rock conductivity 2.5 W/m/K Rock volumetric heat capacity 2.17 MJ/m3/K Canister external diameter 1050 mm Rock wall diameter of the disposal hole 1750 mm Bentonite conductivity in peripherical parts 1.0 W/m/K Bentonite conductivity in central parts 1.1 W/m/K Tunnel backfill conductivity 0.7 W/m/K Width of air gap on copper cylinder 10 mm Width of pellet slot 50 mm Conductivity in pellet slot 1.0 W/m/K Volumetric capacity of pellet slot 1.34 MJ/m3/K Effective conductivity in air gap around canister 0.04 W/m/K Conductivity of copper (also in 3 cm bottom plate) 390 W/m/K Maximum allowed buffer temperature increase 81 oC

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Table 14. Assumed initial data for simulating the SKB analysis for BWR fuel type.

Canister type BWR Burn-up value [MWd/kgU] 40 Pre-cooling time [years] 32.93 Decay heat power at disposal [W] 1 700 Canister height [m] 4.75 Bentonite height above canister [m] 2.9 Bentonite height below canister [m] 0.5 Disposal rate [canisters per year] 36 Heat flux reduction coefficient [-] 0.794

Figure 29. Peak buffer temperature increase vs. canister spacing. The base figure is taken from Hökmark et al. (2009) and curve determined by VTT is added to figure (plotted by big asterisk symbols). VTT’s result is about 2°C on the safe side. Figure 29 shows with large asterisk symbols the curve calculated using values in Tables 13 and 14. The temperature is on the copper surface at the mid-height of the canister. Due to gravity the canister is always in a contact with buffer at some places. Since the

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conductivity of copper is very high (390 W/m/K), the temperature on the surface of the canister is practically constant. Thus the maximum temperature of the buffer equals the surface temperature of the canister. The temperature increase (on the canister surface in the mid-height) is 2-3°C higher than the values presented in the SKB report (tempera-ture increase in the buffer), when the conductivity of rock is 2.5 W/m/K. The differ-ences between the analysis results presented in this report and those published by SKB are acceptable when taking into account the differences in the models (SKB has mod-elled the canister components, too), decay heat (SKB used 38 MWd/kgU) etc. 4.9 Sensitivity to various parameters The sensitivity to various parameters was studied earlier in Ikonen (2009). The effect of emissivity of copper, air gap width, bentonite conductivity and rock conductivity on the maximum canister surface temperature were studied. The study in Ikonen (2009) showed that the emissivity of the copper surface and the conductivity of the bentonite buffer have the greatest effect on the maximum temperature on the canister surface and the needed canister spacing. In this study using the new buffer design it turned out that also the conductivity in the pellet slot is a sensitive parameter.

Figure 30. Effect of pellet slot conductivity on canister spacing. Figure 30 shows the effect of conductivity of pellet slot on canister spacing. In the base case (dry case, maximum temperature 95°C), where the conductivity of the pellet slot is 0.2 W/m/K, change of the conductivity has strong effect on the needed canister spacing. If, for instance, the conductivity is increased from 0.2 W/m/K to 0.3 W/m/K, the allow-

50

able canister spacing is shortened to 0.82 m. In a 30x30 panel this means 713 m saving in tunnel construction. Further investigations of the conductivity of the pellet slot are under way. With the conductivity of the pellet slot higher than 0.7 W/m/K (slot width 50 mm), change of the conductivity do not change any more significantly the needed canister spacing. In the design phase of the bentonite buffer, an air gap was proposed above the canister lid. The effect of this air gap was studied. The heat flux reduction coefficient became k = 0.841 (in the base case 0.829). The canister spacing 8.92 m in the dry base case for BWR canisters had to be increased to 9.18 m for not exceeding the maximum canister surface temperature of 95°C. The difference 0.20 m is so much that the air gap was ex-cluded from the design. In case of EPR canisters the difference would have been even larger, 0.28 m. A copper plate of 30 mm was added to the bottom of the disposal hole (Figure 2). This was a change in comparison to the earlier design. The heat flux reduction coefficient became k = 0.832 (in the base case 0.829). This copper plate decreases the canister spacing from 8.96 m to 8.92 m, only by 4 cm when compared to the earlier design with-out copper plate. In all analyses uniform power generation over the volume of the canister inside of the 50 mm thick overpack was assumed. An alternate way to model the heat generation is to direct uniformly distributed heat flux onto the inner surface of the copper overpack. This gave about 0.8°C higher temperature than the basic case. Thus the effect between the two ways of modelling the heat generation is quite small.

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4.10 Reasoning of temperature margins

The maximum allowable temperature of the bentonite buffer is stated in Design Basis report and is +100°C. The maximum temperature of the canister surface takes place in 10 to 15 years after canister disposal. The saturation of the buffer cannot be guaranteed to happen before the maximum temperature is reached, because the groundwater leaks may vary considerably in various parts of the repository. The thermal dimensioning analysis is made using thermal properties for various materi-als that in general are conservatively selected. The properties of the Olkiluoto rocks that are used are averaged statistical value. However, the temperature dependency of the rock thermal properties is taken into account and the corrected parameter values at temperature +60°C are conservatively used. The average thermal conductivity at +60°C is 2.82 W/m/K. The analysis report for rock thermal properties (Kukkonen et al.2011) gives the standard deviation in thermal conductivity at +25°C as ±0.51 W/m/K. These numbers are based on a few hundred of measured rock samples that are of size of a few millimeters in thickness. From canister cooling point of view, the effective rock thermal properties can be averaged in one meter or tens of meters scale. The larger scale de-creases the variation of the average rock properties. However, when we make sensitiv-ity analyses of the canister temperature having the rock thermal conductivity as a vari-able (see the Appendix B of Ikonen 2009), we can conclude that the maximum tempera-ture is changing by about 0.9°C for every 0.1 W/m/K that the rock thermal conductivity differs from the nominal value. In practice this means that if we had the effective ther-mal conductivity as low as 2.5 instead of 2.82 W/m/K, the maximum temperature would increase +2.9°C. The amount of canister decay power is effectively controlled by the selection procedure for fuel elements to be encapsulated in a single canister. The decay heat for every fuel element is calculated and the elements are selected so that the total decay power is not more than the nominal design power for the canister type. In spite of sophisticated procedure, we estimate the accuracy to be about ±2% in the decay heat estimates. Thus the 2% inaccuracy in the decay heat leads to variation of 2% * 85°C = 1.7°C in the maximum temperature. The 85°C is the average allowable temperature increase of the canister. Of course, the possible inaccuracy in decay heat estimates could be taken into account in the fuel element selection procedure. The two inaccuracies mentioned above (rock conduction variations and estimated decay inaccuracy) lead to summed variation of 2.9 + 1.7 = 4.6°C in maximum temperature in worst combination. Thus it seems reasonable that a margin of 5°C is large enough in maximum calculated temperature, if all the other parameters are selected conservatively. The thermal conductivity of the pellet slot is selected conservatively. The thermal con-ductivity of the pellet slot has given variable values in literature (Kim et al. 2012; Hök-mark et al. 2009) and in tests made lately by Posiva. The pellet slot conductivity esti-mates vary between 0.2 and 0.5 W/m/K and in saturated condition between 1.0 and 1.3 W/m/K. In dry condition analyses used for thermal dimensioning the conservative value 0.2 is used. Later, if the pellet slot conductivity appears to be higher, the analyses may be updated or temperature margin can be increased.

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The thermal dimensioning calculation is made in two assumption sets; first assuming the dry initial condition properties for buffer with 10 mm air gap against canister surface and a pellet slot of 50 mm filled with dry initial condition bentonite pellets, and sec-ondly, assuming that all the buffer components are water saturated and the gaps are closed effectively. For dry condition a margin of 5°C has been selected to allow natural variations in local rock conductivity and to allow the inaccuracy in decay estimate. The postulated dry condition is the determining condition for thermal dimensioning. For saturated buffer condition the actual margin in temperature is more than 15°C in practice.

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5 CONCLUSIONS The objective of this work is to update the basic thermal dimensioning for Olkiluoto repository and to evaluate the effect of different parameters on the highest spent fuel canister temperature and to support the planning, dimensioning and operation planning of the repository in Olkiluoto. In the installation phase of canisters the water saturation rate of the buffer and backfill is low after the manufacture of the bentonite blocks. After closing the tunnels the water content is increased due to groundwater inflow. Due to the swelling of the bentonite, the gap between the buffer and the canister is closed and heat transfer to the rock envi-ronment is improved for this reason. Humidity circumstances in the environment of a canister are difficult to predict. For this reason, the dimensioning of the canister spac-ing is performed for two extremes, the dry and the saturated case. The dimensioning criterion is the maximum temperature on the canister/buffer interface, which due to very good conductivity of copper is practically constant all around the canister surface. The postulated dry conditions for thermal dimensioning are unlikely to exist, especially in long term. The normal expected condition is that the buffer around canisters is water-saturated within shorter time. For this reason it is justified to apply lower safety margin for the maximum temperature in dry conditions than in saturated condition when dimensioning the canister spacings in the repository. The maximum temperature on the canister-bentonite interface is limited to the design temperature of +100°C. For the reasons presented above and further, due to uncertain-ties in thermal analysis parameters (like scattering in local rock conductivity or in pre-dicted decay power) the nominal calculated maximum canister temperature is set to 95°C having a safety margin of 5°C. Correspondingly in saturated condition, which is more probable, maximum nominal temperature is set to 90°C. The nominal temperature is controlled by adjusting the space between adjacent canisters, adjacent tunnels and the pre-cooling time affecting on the decay power of the canisters. For the Olkiluoto repository, the thermal dimensioning is made assuming the canisters to be in rectangular panels of 900 canisters of BWR, VVER or EPR spent fuel. The analyses were performed for each fuel types with an initial canister power of 1700 W, 1370 W and 1830 W, respectively. These decay powers correspond to the average de-cay heat of the spent fuel with pre-cooling time of 32.9, 29.6 or 50.3 years for fuels (with average burn-up of 40, 40 or 50 MWd/kgU, respectively). The analyses gave the resulting canister spacing (7.5-10.5 m), when the tunnel spacing was 25 m.

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Table 15 summarizes the canister spacing in disposal tunnel for EPR, BWR and VVER 440 canisters with 25 m, 30 m and 40 m tunnel spacings, when the analyzed maximum temperature is restricted to 95°C. The report also gives instruction on how long inter-ruption can be allowed between adjacent panel operations without detrimental thermal interaction. Table 15. Canister spacing in disposal tunnel, when the maximum temperature is re-stricted to 95oC.

Canister type and initial power

Tunnel spacing 25 m

Tunnel spacing 30 m

Tunnel spacing 40 m

BWR 1700 W 8.9 m (9.1 m) 8.0 m (8.1 m) 7.2 m (7.3 m) VVER 1370 W 7.5 m (7.3 m) 6.7 m (6.5 m) 6.0 m (5.8 m) EPR 1830 W 10.5 m (10.8 m) 9.3 m (9.5 m) 8.1 m (8.2 m)

Canister spacings obtained in earlier analysis of Ikonen (2009) are given in brackets. The earlier, more conservative values can still be applied. If the knowledge of the thermal conductivity data from bentonite pellet slot will be es-sentially changed later, the dimensioning analysis may be updated.

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REFERENCES Andersland, O., Anderson, D., 1978. 1927- Geotechnical engineering for cold regions. McGraw-Hill, New York. Anttila, M. 2005. Radioactive Characteristics of the Spent Fuel of the Finnish Nuclear Power Plants. Working Report 2005-71. Posiva Oy, Olkiluoto. 20 p + App. 310. Börgesson, L., Fredriksson A., Johannesson L-E. 1994. Heat conductivity of buffer materials. SKB TR-94-29. Fletcher, C.A.J. 1991. Computational Techniques for Fluid Dynamics. Volume I. Se-cond edition. Springer-Verlag. 401 s. Hautojärvi, A., Anttila, M. & Taivassalo, V. 1987. Effects on fuel burn-up and cooling periods on thermal responses in a repository for spent nuclear fuel. Report YJT-87-21. Technical Research Centre of Finland. 32 p. Hökmark, H., Sundberg, J., Hellström, G. 2009. Strategy for thermal dimensioning of the final repository for spent nuclear fuel. SKB Report R-09-04. December 2009. 154 p. Ikonen, K., 2006. Fuel temperature in disposal canisters. Working Report POSIVA 2006-19. Posiva Oy, Olkiluoto. 47 p. Ikonen, K. 2009, Thermal dimensioning of spent fuel repository. Working Report POSIVA 2009-69. Posiva Oy, Olkiluoto. 59 p. Kim, C-S., Man, A., Dixon, D., Holt, E., Fritzell, A., 2012. Clay-Based for Use in Tun-nel Backfill and as Gap Fill in a Deep Geological Repository: Characterization of Thermal-Mechanical Properties. NWMO TR-2012-05. May 2012. p. 83 + 28. Kukkonen, I, Kivekäs, L., Vuoriainen, S. Kääriä, M., 2011. Thermal properties of rocks in Olkiluoto: Results of laboratory measurements 1994-2010. Posiva Oy, Olkiluoto. Working Report 2011-17. 96 p. Mills, A.E. 1999. Basic heat & mass transfer. 2nd edition, Prentice Hall, 1999, ISBN 0-13-096247-3. Raiko H. 2012. Canister Design 2012. Report POSIVA 2012-13, Posiva Oy. Ryti, H. 1973. Heat and mass transfer. Technical handbook. K.J. Gummerus Osake-yhtiö. Vol. 1, pp. 357-424. (in Finnish). Saanio, T. (ed), Ikonen, A., Keto, P., Kirkkomäki, T., Kukkola, T., Nieminen, J., Raiko, H. 2012. Loppusijoituslaitoksen suunnitelma 2012. Posiva Working Report 2012-50. Posiva Oy. Safety case for the disposal of spent nuclear fuel at Olkiluoto – Design Basis 2012. Posiva 2012-03. ISBN 978-951-652-184-1.

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Safety case for the disposal of spent nuclear fuel at Olkiluoto – Performance Assessment 2012. Posiva 2012-04. ISBN 978-951-652-185-8.

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APPENDIX: NEAR AND FAR FIELD CALIBRATION WITH A SINGLE FUEL CANISTER The objective of this appendix is to calibrate the analytical line heat source model by the analytic model in order to use it for analysing the whole spent fuel repository. The canister maximum surface temperature is the most important output quantity. The cali-bration is based on the comparison of the results obtained by the control volume solu-tion of a single canister. The gaps are taken into account as described in Chapter 3.3. Figure 1 shows the grid of the numerical axi-symmetric model of the BWR canister area and the surrounding rock. The colours present different materials.

Figure 1. Axi-symmetric model of BWR canister with the basic mesh and with two and three times denser mesh. Grid and material types (canister red, bentonite yellow, tun-nel green and rock blue). The edges of the mesh is not necessary to extend very far, since the temperatures on the edge nodes can be calculated from analytic solution 18. Actual canister and its envi-ronment differ from ideal line source model, but this effect extends only to very near around the canister. The edges can be only some meters from the canister. In calculation of actual spent fuel repository, which consists a great number of canisters and for which the numerical model would be very large, analytic model is much more efficient. Air gap is assumed only on the cylindrical copper surface of the canister. Due to grav-ity forces straight contact is assumed on the lower and upper lids. The conductivity and the capacity of air are calculated from the fittings (1). Table 1 presents data for the numerical analysis and it presents also the data used in the line heat source model. Since the conductivity of pellet slot is lower than the conductiv-

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ity of the rock, the maximum value of 50 mm for the width of the pellet slot is chosen. This case is geometrically identical with an actual BWR canister. Table 1. Initial data for the analysis of the BWR canister in the base case.

Burn-up value 40 MWd/kgU Pre-cooling time 32.95 years Decay heat when disposed 1700 W Amount of uranium in a canister 2.11 tU Canister height 5.20 m Canister external diameter 1050 mm Rock wall diameter 1750 mm Initial undisturbed rock temperature 10.5 °C Canister initial temperature 50 °C Canister overpack conductivity 390 W/m/K Bentonite buffer conductivity 1.0 W/m/K Bentonite volumetric heat capacity 3.52 MJ/m3/K Rock volumetric heat capacity 2.2 MJ/m3/K Rock volumetric heat capacity 2.10 MJ/m3/K Buffer volumetric heat capacity 2.4 MJ/m3/K Bentonite buffer thickness below canister 500 mm Bentonite buffer thickness above canister 2900 mm Bentonite surface emissivity 0.8 - Canister surface emissivity 0.3 - Width of air gap on copper surface 10 mm Bentonite conductivity 1.0 W/m/K Conductivity of pellet slot 0.2 W/m/K Volumetric capacity of pellet slot 1.34 MJ/m3/K Rock conductivity at 60oC 2.82 W/m/K Width of pellet slot between buffer and rock 50 mm

Decay power of BWR fuel is presented as described in Chapter 2.4. Decay heat 1700 W at disposal is reached after 50.32 years pre-cooling time in case of 40 MWd/kgU burn-up. Canister initial temperature (50°C) is not an essential parameter, since the canister initial temperature reaches the stationary temperature within only some days. Applied temperature dependence of the conductivity and volumetric heat capacity of air are shown in Figure 5. Figure 1 illustrates the grid and material types (a) and temperature distribution after 2.0 years (b). In the model there are 3064 control volumes. Time steps are 100 s, 900 s and

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1800 s, when the actual time is 0 < t ≤ 10 hours, 10 hours < t ≤ 10 hours and t > 10 hours, respectively. The canister was assumed to be homogeneous with uniform power generation over its volume inside of the 50 mm thick overpack and the contents of it was not modelled in detail, since the copper shell has very high thermal conductivity (390 W/m/K) causing practically uniform temperature distribution on the external sur-face of the canister. Figure 9b later shows that the temperature distribution pattern is symmetrical with the horizontal plane passing through the middle of the canister. Thus different height of the buffer above and below the canister and the different conductivity of the tunnel backfill material have minor effect. The line heat source model may thus estimate successfully the temperature in the mid-height of the canister, where the highest temperature is en-countered. In the figures below the temperature is considered in the mid-height the canister. Since the conductivity of copper (390 W/m/K) is very high, the temperature on the surface of the canister is practically constant. Due to gravity the canister is always in a contact with buffer at some places. Thus the maximum temperature of the buffer equals the surface temperature of the canister and the curves on the copper surfaces the figures below concern also the maximum temperature of the buffer.

Figure 2. Temperature history on canister surface and on rock wall. BWR fuel.

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Figure 2 presents the temperature evolution on the canister surface in the mid-height of the canister and on the corresponding height on the rock wall. Temperatures obtained analytically from Equations 8 and 18 (effective height is applied!) are greater than nu-merically calculated, which is caused by the fact that the analytic solution does not take into account the insulating effect of the air gap and bentonite. Figure 2 shows that the analytic and numerical solution give quite accurately equal temperature histories for the rock wall temperature Trock. The fact that the numerically and analytically calculated temperature histories on the rock wall are nearly equal, is an important result, since it proves that the analytic solution using effective canister height and only rock material, several canisters can be superposed even if they are close to each others. In practice the distance between the canisters is more than seven meters. According to numerical solution maximum temperature on the single canister surface is 82.7°C after 1.33 years with the basic mesh. Temperatures 83.31°C and 83.47°C are obtained by two and three times denser meshes. Analytic solution gave the maximum temperature 83.3°C (this was increased further to 90.5°C, when the actual height of the canister was used instead of the effective height). Numerical solution gave 38.16°C for the maximum temperature after 2.6 years on the rock wall. Numerical solution tem-peratures 38.38°C and 38.43°C are obtained by two and three times denser meshes. Analytic solution gave for the maximum temperature 39.8°C (this was increased further to 41.5°C, when actual height of the canister was used instead of the effective height) after 1.9 years. The analytic solution (k = 1) gives 7.2°C higher temperature on the canister surface than the numerical solution without calibration. The shape of the curves calculated numeri-cally and analytically are very similar and the curves coincide, if the mean heat flux in the analytic Equation 18 is reduced by the coefficient k. The coefficient is determined by changing k as far as the maximums are sufficiently close to each other. This gave the parameter value of k = 0.814. The corresponding curve is plotted in Figure 3. Us-ing two and three times denser meshes heat flux reduction coefficients 0.826 and 0.829 were obtained.

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Figure 3. Numerically and analytically calculated radial temperature profiles in the mid-height of the canister after 1.33 years, when the highest canister surface tempera-ture of 82.7°C (in analytic solution k = 0.814) is encountered. Figure 3 shows the detailed radial temperature profile after 1.33 years in the mid-height of the canister, when the highest canister surface temperature of 82.7oC is encountered. Numerical and analytical profiles correspond well on the areas of the canister and bentonite, when the heat reduction coefficient k = 0.814 (with the basic mesh) is applied and determined as described earlier. In numerical solution the temperature T0 on the canister surface after 1.33 years is T0 = Trock + ΔTpel + ΔTben + ΔTairgap = 37.8°C + 12.4°C + 18.3°C + 14.2°C = 82.7°C. In case of several canisters the shape of the near-field temperature profile in Figure 3 re-mains practically unchanged. It is only elevated to higher level of about 5…20°C de-pending on the canister and tunnel spacing and disposing rate.

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Figure 4 presents the difference of the temperatures in Figure 3 between analytically and numerically calculated radial temperature profiles after 1.33 years. No difference exists on the surface of the canister, since the calibrated equality of the temperatures is set in that point. The greatest difference 1.8°C is encountered on the rock wall and the difference decreases and for instance it as about 0.6°C, when the radius is 1.8 m. These quite small temperature differences have no effect on the canister surface temperature. Also with other times good agreement is achieved by using equal heat reduction coeffi-cient. As stated above, also the curves of temperature vs. time on the canister surface coincide precisely.

Figure 4. Difference between analytically and numerically calculated radial tempera-ture profiles after 1.33 years.

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Figure 5. Heat flux distribution along canister external surface starting from the centre of the lower lid and ending to the centre of the upper lid after 1.33 years. Figure 5 shows heat flux distribution along canister external surface after 1.33 years. The highest heat flux is reached in the corners of the canister, where the space angle to the bentonite direction is largest. The temperature derivative is highest in outwards di-rection, which can be seen also from Figure 9b. Thermal flux φ0 in the mid-height of the canister is about 89% from the average heat flux φmean on the canister surface. In the corners there is peak in the heat flux curve, since the corner works like a cooling fin. From Figure 5 it can be found that heat flux has its lowest value 75.5 W/m2 in the upper corner and 80.4 W/m2 in the middle of the canister cylinder. After 1.33 years the decay heat of the canister is 1659 W. By dividing this by the external area of 17.4 m2 for the mean flux 95.3 W/m2 is obtained. By dividing the heat flux 80.4 W/m2 by 95.3 W/m2 for the ratio 0.844 is obtained, which is 3.6% greater than the heat flux reduction coeffi-cient k = 0.814 (basic mesh density). The difference is caused e.g. from the fact that the calculation of the heat flux from the copper surface having high conductivity is numeri-cally inaccurate.

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Figure 6. Temperature distribution on copper surface starting from the middle of the lower lid and ending to the middle of the upper lid. Figure 6 presents the temperature distribution on the copper surface. In the middle of the cylinder the temperature is 82.7°C and in the corners 81.8°C. The difference is only 0.9°C. The differences are thus very small. This is caused by very high conductivity of the copper overpack (390 W/m/K). The conclusion of above is that the internal parts of the canister are not needed to be modelled in detail, although the maximum temperature in individual fuel pellets is about 200°C Ikonen (2006). The canister can be treated as a homogeneous cylinder having a uniform conductivity and internal heat generation.

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Figure 7. Temperature distribution on copper surface and on the inner surface of bentonite buffer. Figure 7 presents the temperature distribution on the copper surface and on the inner surface of bentonite. On the lids the temperatures are equal because of the assumption of straight contact. On the cylindrical area the temperature fluctuates about 2°C on the bentonite surface.

Figure 8. Evolution of energy balance error. An important checking point in calculation process after every time increment is the en-ergy balance requirement: total energy penetrating the outer surfaces + change of the

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enthalpy of the model should equal the energy generated inside the model. Figure 8 presents the evolution of the energy balance error. The error is mostly caused by the inaccuracies on the edges of the model. If the edges were insulated the error would be very small, but thermal impulses were reflected from the edges causing incorrect tem-perature in longer term. As mentioned above the temperature on the outer edges of the model are solved from Equation 8.

(a) (b)

Figure 9. Temperature distribution BWR canister after about 1.33 years, when copper surface reaches its maximum 82.7°C in the mid-height of the canister. In the basic model there are 1776 nodes (control points) and 1708 elements. Figure b shows that the shape of temperature field is changed from an ellipsoid to a sphere when going farer from the canister. On white isotherm temperature is 11.0°C (10.9°C-11.1°C) and on pink isotherm 15.0°C (14.5°C-15.5°C).

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Figure 10. Temperature distribution of BWR canister after 1.33 years, when the mesh is two and three times denser than in the basic case. In the models there are 6669 and 12606 nodes (control points) and 6536 and 12420 elements (in the basic model 1776 nodes and 1708 elements). Copper surface reaches its maximum 83.31°C and 83.47°C in the mid-height of the canister. The effect of the mesh density was investigated by two and three times denser meshes (Figure 10). For the maximum temperature was obtained 83.31°C and 83.47°C after 1.33 years (with the basic mesh 82.72°C after 1.33 years). For the heat flux reduction coefficient values k2 = 0.826 and k3 = 0.829 (with the basic mesh k1 = 0.814) were ob-tained. For the rock wall temperature was obtained 38.38°C and 38.43°C (with the ba-sic mesh 38.16°C). Mesh density has thus a minor effect. In the spent fuel panel in Chapter 4 (Table 4) the value k3 = 0.829 for the BWR canister is used in the analysis to obtain the correct canister surface temperature in the mid-height of the canister.

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Figure 11. Temperature histories without air gap. Figure 11 presents temperature histories without air gap and with the basic mesh. The shape of the curves is similar to in case with air gap (compare to Figure 2). Due to straight contact and improved heat transfer the temperature on the canister surface is lowered. The heat reduction coefficient k = 0.822 is a little greater than the coefficient with air gap, k = 0.814.

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Figure 12. Numerically and analytically calculated radial temperature profiles in the mid-height of the canister after 1.78 years without air and pellet gaps and with bento-nite conductivity 1.3 W/m/K, when the highest canister surface temperature of 57.9°C (in analytic solution k = 0.822) is encountered. Figure 12 shows the detailed radial temperature profile after 1.78 years in the mid-height of the canister without air and pellet gaps and with saturated bentonite conduc-tivity 1.3 W/m/K (compare Figure 3), when the highest canister surface temperature of 57.9°C is encountered. Numerical and analytical profiles correspond well to the areas of the canister and bentonite, when the heat reduction coefficient k = 0.822 is applied. Maximum temperature on the canister surface is T0 = Trock + ΔTben = 38.8°C + 19.2°C = 57.9°C. This gives the temperatures in case that bentonite buffer is water-saturated. The canister surfaces temperature is 24.8°C lower than in case with air gap (82.7oC, Figure 2) and with bentonite conductivity 1.0 W/m/K.

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Conclusion from calibration analyses

The analytical model was calibrated by comparing the results from analytical and nu-merical axisymmetric analyses for a single BWR canister. The analytical result con-cerning a line heat source with homogeneous material can be extended to analyze an actual canister with finite radius and different materials by calibrating the heat flux re-duction coefficient k of the mean flux on the cylinder surface. The calibrating heat flux reduction coefficient k is the reduction coefficient of the mean heat flux giving the heat flux in the mid-height of the canister. The parameter k is adjusted to give equal canister surface temperature histories by the analytic and numerical models. For the BWR, VVER and EPR canisters the values kBWR = 0.829, kVVER = 0.811 and kEPR = 0.833, were obtained with three times denser mesh than the basic mesh. These values were used in the analysis (see Table 4 in the main text). The fact that the numerically and analytically calculated temperature history on the rock wall at the disposal hole are equal is an important result, since it proves that the analytic solution of several canisters can be superposed even if they are very close to each oth-ers. In practice the distance between canisters is more than seven meters. Superposing of single analytical line heat sources the temperature field of the whole repository can be determined efficiently. Figures 3 and 4 showed that the radial temperature and temperature histories on the canister surface and on the rock wall are very similar. This demonstrates that the ana-lytic solution 18 gives good results, when only k is calibrated. In the depth of 400 m the ambient rock temperature in Olkiluoto is +10.5°C and the am-bient temperature increases +1.5oC per 100 meters in the depth direction. Using of heat flux reduction coefficient is not the only possibility to take the differences between the actual canister and the idealized line source model into account. It would be also possible to calculate the temperature far from a canister caused by all the canis-ters and then use the data obtained from the numerical solution near the canister in order to determine the temperature of the canister surface. However, then temperatures from different places were necessary (temperature canister surface in sufficient in practise) to store and from different times. An additional problem comes from that heat is different in different canisters in actual disposal. Using of heat flux reduction coefficient is how-ever more practical, since only one coefficient is sufficient for calculating temperatures on canister surfaces.

Thermal Dimensioning of Olkiluoto Repository for Spent · PDF fileTHERMAL DIMENSIONING OF OLKILUOTO REPOSITORY FOR SPENT FUEL ABSTRACT This report contains the updated temperature

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