atw 2018-05v6

inforum

atw Vol. 63 (2018) | Issue 5 ı May

(a) Parameter variation: t cool

(b) Parameter variation: k

(c) Parameter variation: D 1

DECOMMISSIONING AND WASTE MANAGEMENT 324

60 u(t,P) [°C]

50

40

30

20

10

0

0 1 10 10 2 10 3 10 4 10 5

60 u(t,P) [°C]

50

40

30

20

10

0

33 y

66 y

100 y

200 y

300 y

(d) Parameter variation: D 2

0 1 10 10 2 10 3 10 4 10 5

60 u(t,P) [°C]

50

40

30

20

10

0

8.9 m

10 m

12 m

16 m

asymp.

(g) Parameter variation: n, D 1 , D 2

30, 25 m, 8.9 m

10, 40 m, 12 m

10, 40 m, 15 m

1, −, 15 m

asymp.

0 1 10 10 2 10 3 10 4 10 5

| | Fig. 4.

Time [y]

Temperature evolution at P = P 3 for the baseline

configuration C b (black) and alter native

configurations (blue). Panels a-f: One parameter

changed (parameter in title); g: Three

parameters changed. Host rock composition:

crystalline rock with isotropic heat conductance

2.82 W/mK, heat capacity 2.09 MJ/m 3 K.

D 1 and D 2 (Figure 2). Instead, changes

in n and s lead to more substantial

thermal benefits. Changes in k result

in an intermediate situation. In this

sense, it can be said that action on t cool ,

D 1 and D 2 mainly lead to short-term

thermal benefits, while action on n

and s lead to long-term benefits. A

comprehensive thermal dimensioning

should therefore include action on

parameters from both groups.

Figure 3 shows the temperature increase

at a point P 2 sited 20 m above

the repository centre in the baseline

configuration C a for argillaceous rock,

as well as for parameter variations

thereof. P 2 is of relevance for the

admissibility of pore water pressure

resulting from the increase in temperature.

At this point, the temperature

raises by 49 °C within 500 y and

decreases thereafter. Regarding efforts

and benefits, the discussion is qualitatively

identical to the dis cussion of

Figure 2. Differences are mainly

quantitative in nature. For example,

the asymptotic limits (dashed, blue)

60 u(t,P) [°C]

50

40

30

20

10

0

0 1 10 10 2 10 3 10 4 10 5

60 u(t,P) [°C]

50

40

30

20

10

0

k = 9

k = 6

k = 3

k = 1

(e) Parameter variation: n

0 1 10 10 2 10 3 10 4 10 5

Time [y]

n = 30

n = 6

n = 3

n = 1

for D 1 → ∞, D 2 → ∞,

n = 1 and s → 0 are considerably

smaller at P 2 than at P 1 . For D 2 and s

they almost vanish. One important

aspect for the present discussion is the

observation that action on D 1 and n

leads to comparatively greater benefits

for the same effort at P 2 than at P 1 . For

example, at P 2 , peak temperature

decreases by a factor of 1.8 (from 48 °C

down to 26 °C) when passing from

n = 27 to n = 3. The same action at P 1

results in a benefit of a factor of 1.1

only (from 65 °C down to 58 °C). In

Figure 3a-f, only a single engineering

parameter has been changed at a time.

Results for alternative configurations

with n decreased and D 1 , D 2 increased,

other parameters unchanged, are

shown in Panel g. The graphs show

that considerably lower temperatures,

even approaching the asymptotic case,

can be envisaged if sufficient space is

reserved to allow for reasonable action

on D 1 , D 2 and n.

Qualitatively similar findings apply

to point P 3 and to the case of a repository

sited in crystalline rock with

configuration C b (Table 3b, Figure 4).

Altogether, the results indicate that

the patterns of interdependence

between spatial and thermal dimensioning

are non-trivial and cannot be

parameterised by the space-averaged

heat load alone. For example the

average initial heat loads for D 1 =

80 m in Figure 2c and for D 2 = 15 m in

Figure 2d are both close to 2.2 W/m 2 ,

yet their peak temperatures differ by

more than 12 °C.

Conclusions

There is a close interdependence

between spatial and thermal dimensioning

of disposal facilities for

60 u(t,P) [°C]

50

40

30

20

10

0

0 1 10 10 2 10 3 10 4 10 5

60 u(t,P) [°C]

50

40

30

20

10

0

25 m

30 m

50 m

60 m

asymp.

(f) Parameter variation: s

0 1 10 10 2 10 3 10 4 10 5

Time [y]

30 x 30

21 x 21

12 x 12

3 x 3

1 x 1

high­ level radioactive waste and spent

fuel and an important potential for

further reduction of the transient

temperature peak, resulting in supplementary

thermal benefits. After a few

decades of cooling storage, the most

efficient adjusting screws for thermal

dimensioning beyond strict admissibility

are drift spacing D 1 , batch spacing

D 2 and number of drifts n. Action

on batch charge k results in large

benefits but also large efforts to obtain

them. Cooling storage becomes

rapidly less efficient as cooling time

t cool increases. Dividing the repository

into clusters is inefficient with regard

to the reduction of peak temperatures

unless clusters are made very small.

Action on t cool , D 1 and D 2 leads to

short-term thermal benefits, while

action on n and s to long-term thermal

benefits. Except for t cool , all options

are related to geometrical side-effects

that increase space requirement. If, in

the current process of site selection,

spatial reserves are limited tightly in

proportion to space-saving configurations,

the options for final thermal

dimensioning by action on D 1 , D 2 , k, n,

and s in later project phases are

severely reduced. If on the other hand,

the scope for action on these parameters

is preserved, considerably cooler

repository designs remain possible in

later project phases. Therefore, the

preservation of technical options for

final thermal dimensioning should

always be part of early decisionmaking

in the site selection process.

This particularly applies for temperature-sensitive

configurations in argillaceous

or crystalline rock. It should

equally apply to rock salt when

retrievability of waste is legally

required.

Decommissioning and Waste Management

Scope for Thermal Dimensioning of Disposal Facilities for High-level Radioactive Waste and Spent Fuel ı Joachim Heierli, Helmut Hirsch, Bruno Baltes

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