atw 2018-05v6

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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 322

60

50

40

30

20

10

0

60

50

40

30

20

10

0

60

50

40

30

20

10

0

u(t,P) [°C]

55 y

100 y

200 y

300 y

450 y

0 1 10 10 2 10 3 10 4 10 5

u(t,P) [°C]

(d) Parameter variation: D 2

7.6 m

9 m

11 m

15 m

asymp.

0 1 10 10 2 10 3 10 4 10 5

u(t,P) [°C]

(d) Parameter variation: D 2

7.6 m

9 m

11 m

15 m

asymp.

0 1 10 10 2 10 3 10 4 10 5

| | Fig. 2.

Temperature evolution at P = P 1 for the

baseline configuration C a (black) and

alternative configurations (blue).

A-F: One parameter changed (parameter

in title); G: Three parameters changed.

Host rock composition: opalinus clay (argile)

with anisotropic heat conductance 1.2 W/mK

(vertical), 2.15 W/mK (horizontal), heat

capacity 2.3 MJ/m 3 K.

60

50

40

30

20

10

0

60

50

40

30

20

10

0

u(t,P) [°C]

k = 4

k = 3

k = 2

k = 1

0 1 10 10 2 10 3 10 4 10 5

u(t,P) [°C]

(e) Parameter variation: n

0 1 10 10 2 10 3 10 4 10 5

Time [y]

n = 27

n = 7

n = 3

n = 1

Param. Value Benefit / unit

t cool

55 y

100 y

200 y

k 4

3

2

D 1

D 2

40 m

50 m

60 m

7.6 m

9 m

11 m

n 27

7

3

(a)

0.25 °C/y

0.14 °C/y

0.07 °C/y

16 °C/FE

16 °C/FE

16 °C/FE

1.3 °C/m

0.5 °C/m

0.2 °C/m

6.8 °C/m

5.1 °C/m

3.4 °C/m

-0.1 °C/row

0.7 °C/row

5.5 °C/row

0 1 10 10 2 10 3 10 4 10 5

| | Tab. 2.

Expected benefit on peak temperature per unit change of a parameter, starting with the baseline

configuration. (a) Configuration C a ; (b) Configuration C b .

Example for case (a): Increasing t cool = 55 y by one year yields a benefit of 0.25°C. Extending D 2 by 1 m

results in a benefit of 6.8 °C (27 times more in comparison). FE = “fuel element.”

60

50

40

30

20

10

0

60

50

40

30

20

10

0

u(t,P) [°C]

u(t,P) [°C]

(f) Parameter variation: s

Time [y]

40 m

50 m

60 m

80 m

asymp.

27 x 81

15 x 45

9 x 27

3 x 9

1 x 1

0 1 10 10 2 10 3 10 4 10 5

Param. Value Benefit / unit

t cool

55 y

100 y

200 y

k 4

3

2

D 1

D 2

40 m

50 m

60 m

7.6 m

9 m

11 m

n 27

7

3

(b)

0.25 °C/y

0.14 °C/y

0.07 °C/y

16 °C/FE

16 °C/FE

16 °C/FE

1.3 °C/m

0.5 °C/m

0.2 °C/m

6.8 °C/m

5.1 °C/m

3.4 °C/m

-0.1 °C/row

0.7 °C/row

5.5 °C/row

at P 1 increases to 100 °C in a few decades,

peaks at 103 °C after 316 y and

remains in this range for several hundred

years (Figure 2, black curves).

Examination of Figure 2 leads to the

following observations.

The increase of cooling times is an

efficient option for reducing peak

temperature, but beyond a few

decades the benefits rapidly decrease

(Figure 2a, Table 3a). As t cool is raised

from 55 y to 100 y for example, peak

temperature decreases by 8 °C, representing

a benefit of 1.8 °C per decade.

A further rise to 300 y decreases peak

temperature by another 16 °C, representing

a benefit of 0.8 °C per decade.

For comparison, increasing t cool from

30 y to 55 y represents a benefit of

5.5 °C per decade. The rate of heating

decreases with increasing cooling

times, which is beneficial for retrieval

in the first few hundred years, but

peak time increases (the time for

which peak temperature is attained).

On the detriment side, intermediate

storage of large inventories on the

land surface represents a considerable

effort and is vulnerable to natural

or human-made hazard, including

malicious acts. Its deployment requires

monitoring, inspection, maintenance,

repair and, not least, a stable

society.

The reduction of batch charge k

leads to a reduction of peak temperature

by about 16° per fuel

element, while peak times roughly

remain constant (Figure 2b). The

considerable thermal benefits are

associated with high efforts as a

greater number of batches have to

be manufactured and handled over

farther distances, with possible

adverse effects regarding occupational

safety. Accordingly, the disposal

area and total drift length increases.

For example, the effort for decreasing

batch charge from 4 fuel elements to 1

implies quadrupling the number of

waste containers and quadrupling the

total length of the disposal drifts

altogether. For these reasons, the

benefit-to-effort ratio decreases as

k is reduced.

Increasing the spacing of disposal

drifts leads to a substantial reduction

of peak temperature as D 1 is increased

from 40 m to 50 m, but the positive

trend markedly decreases thereafter

(Figure 2c). Further reduction practically

stops at u = +50 °C. Accordingly,

the reduction of peak temperature

per meter drift spacing is important

for small D 1 and almost inexistent for

large D 1 (Table 3a). On the positive

side, the temperature peak becomes

narrower for high D 1 , with peak time

occurring earlier. Counting 316 y to

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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