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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