atw 2018-05v6


atw Vol. 63 (2018) | Issue 5 ı May


Access gallery

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disposal area (1 cluster)

waste batches

disposal area (1 cluster)

waste batches

| | Fig. 1.

Spatial layout for (a) configuration C a and (b) configuration C b . The disposal area can be divided in more

than one cluster. Red: center batch of cluster.

unlimited in time, has recently been

considered by the Nuclear Energy

Agency [OECD-NEA 2012] and is

required by national law in an increasing

number of countries (e.g. Finland,

Germany, Switzerland). As temperatures

increase fast after waste

emplacement, the ambient conditions

for waste retrieval give rise to operational

uncertainties, which should be

taken into account in an early stage of

planning [Heierli and Genoni 2017].

Last but not least, it has been pointed

out that hotter repository designs are

intrinsically more complicated and

that their uncertainties in behaviour

are too large to accept [Long and

Ewing 2004; Whipple et al. 1999].

The trade-offs and uncertainties

are to be analysed in safety cases. The

purpose of the safety cases is to

determine whether an adequate level

of confidence in safety can be achieved

and whether the safety criteria can be

fulfilled [IAEA 2012]. An important

aspect hereby is that the temperature

of components remains within boundaries

determined in safety analyses.

Formally, this step is handled by using

criteria of admissibility in the form of

inequalities [e.g. Hökmark et al. 2009;

Eikemeier et al. 2013; Ikonen and Raiko

2012; Jobmann et al. 2016; Kommission

Lagerung hoch radioaktiver Abfallstoffe

2016]. Unilateral criteria do no

bring about a unique solution, however,

but a scope of admissible choices.

To select amongst those, the prevailing

procedure is to take into account

the use of spatial resources underground,

resulting in setting the space

requirements as high as judged necessary

and as low as judged possible.

drifts (n)



drifts (n)





Currently, many national disposal

programmes are in the stage of siteselection.

In this stage, site boundaries

are determined under the leadership

of national governments. In order

clarify the challenges of the corresponding

decision-making process,

this contribution explores the interdependence

between spatial and

thermal dimensioning. Temperatureaffecting

design options are parameterised

to evaluate their benefit on

the one side and the engineering

effort to realise that benefit on the

other. It is emphasised that neither the

optimisation of peak temperatures nor

the optimisation of spatial resources

are the primary objectives of nuclear

waste disposal. It is understood

Project leadership

| | Tab. 1.

Baseline configuration of study cases (10,15). SF = “spent fuel.”


20 m

0.88 m



1.5 m

throughout this work that the main

objective is to enhance both the safe

confinement of waste and the confidence

in the functionality of its


Materials and method

The configuration of a repository for

high-level waste and spent fuel can be

represented by a configuration vector

C = (x 1 , x 2 , …) of engineering parameters

x i (Figure 1). In the present

context, of interest are those that

affect temperatures most. These are:

the cooling time from reactor retrieval

to disposal of the waste (t cool ), the

number of fuel elements per waste

batch (k), the spacing of disposal

drifts (D 1 ), the spacing of batches

within a drift (D 2 ), the number of

disposal drifts (n) and the size of

sub-clusters of batches for disposal

(s). Parameters that are not freely

adjustable by the engineers, such as

the total amount of waste to be

disposed or the depth of the repository,

are not varied in this study.

Let P i be a decision point for the

dimensioning of temperature in a

component indexed i, e.g. the canister

core, the canister surface, the backfill

material, the ambient rock, the

nearest significant aquifer, etc. For

each P i , there exists a decision

criterion T 0 (P i ) + u(t, P i ) < T i , where

T 0 (P i ) is the undisturbed temperature

at P i , u(t, P i ) is the temperature

increase at P i at time t. The right-hand

side term T i is the admissible boundary

temperature for the component

at P i . A configuration C = (n, t cool , k,

D 1 , D 2 , s, …) is considered admissible

if the criterion is satisfied for all P i .


C a


C b


Type of host rock (fixed) clay crystalline

Depth of the repository (fixed) 650 m 420 m

SF type (fixed) UO 2 +MOX UO 2

burnup (fixed) 48 MWd/kg 40 MWd/kg

Cooling time of SF t cool 55 y 33 y

Initial average decay power per SF element π 0 (t cool ) 337.5 W 189 W

Number of SF elements for disposal (fixed) F 8748 8100

Number of SF elements per batch k 4 9

Initial average decay power per waste batch p 0 = kπ 0 1350 W 1700 W

Number of disposal drifts n 27 30

Number of batches per disposal drift m 81 30

Number of batches total N= F/k = nm 2187 900

Spacing of disposal drifts D 1 40 m 25 m

Spacing of batches within a drift D 2 7.6 m 8.92 m

Cluster size s 27×81 30×30

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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