atw 2018-05v6

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atw Vol. 63 (2018) | Issue 5 ı May DECOMMISSIONING AND WASTE MANAGEMENT 320 Access gallery Access gallery 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) (a) (b) drifts (n) D1 D2 D1 D2 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.” P2 20 m 0.88 m P3 P1 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 elements. 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 . symbol C a Nagra C b Posiva 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
atw Vol. 63 (2018) | Issue 5 ı May The fulfilment of the admissibility conditions, however, is not the endpoint of engineering endeavor. Supplementary benefits may be achiev able within reasonable efforts. It is therefore important to explore repo sitory configurations beyond their strict admissibility. Since every disposal project needs to fulfil particular national regulations, it is not possible to address all situations at once. In the following, two situations shall be considered as examples to illustrate the interdependence between spatial and thermal dimensioning: (1) A facility planned for argillaceous rock in northern Switzerland by the Swiss National Cooperative for the Disposal of Radioactive Waste (Nagra), with baseline configuration C a (Table 1). This project is currently in the stage of site-selection under the supervision of the Swiss Federal Office of Energy. (2) A facility targeted for crystalline rock in southern Finland by the Finnish expert organisation for nuclear waste management (Posiva Oy), with baseline configuration C b (Table 1). This project has been approved by the Finnish Radiation and Nuclear Safety Authority. The thermal dimensioning of a repository for high-level waste and spent fuel requires the mutual comparison of a large number of engineering configurations comprising large amounts of individual heat sources. Therefore, the evolution of temperature at decision-critical points P i must be evaluated in reasonable CPU time. For the purpose of this study, a computational model based on the numerical integration of analytically calculated Green’s functions for all relevant heat sources has been implemented [Carslaw and Jaeger 2011; Myers et al. 2015; Heierli 2016]. The method remains insensitive to length scales, which greatly facilitates parameter studies. The purpose of the Green’s function model is to predict the temperature increase u(t,P) within a few degrees Kelvin at location P and time t in a homogeneous (but not necessarily isotropic) volume of the circumambient rock to a repository of arbitrary configuration. The model is not designed to compute the temperature in engineered components such as tunnel lining, inside the backfill or waste containers, nor in remote rock formations. The positions of heat sources in the repository are modelled in 3 dimensions. The (real) heat sources are supplemented by (imaginary) images sources to account for isotherm conditions on a given boundary surface, e.g. the earth surface in the present work. The image sources are sited on the mirror image of the repository with respect to the boundary surface. The instant power release of each image source is equal and opposite in sign to the power release of the corresponding heat source. The heat sources and the image sources are modelled in dependence to their distance to P. Sources sited remotely from the point of observation are modelled as single point sources, whereas nearby sources are modelled as a mesh of points sited on the surface of the waste canister, to account for container geometry. By virtue of the superposition principle, contributions from the repository are treated separately from those originating from geothermal heat. Aspects of secondary importance are omitted in the model: It is assumed that the radioactive decay of the activated waste represents the dominating source of heat in the repository. Other sources or sinks, such as enthalpy of reactions taking place underground, initial heat content of waste canisters, ventilation and construction of caverns are neglected. Heat is conservatively assumed to be transported by conduction. Thermal properties are assumed invariant in time. Waste disposal is assumed to take place instantly, rather than in a period of one or two decades. The geometry is assumed to remain stable over the time range considered. Further implementation details are given in Heierli [2016]. The main advantage of the Green’s function method is that the temperature at an arbitrary point in the underground can be computed independently of the temperature of any other points at previous times, resulting in a fast algorithm allowing for the calculation of a large variety of configurations. The CPU time for the simulation of the configurations considered in this study, calculated over 100’000 y in full 3D for P, range between 30 s and 1 minute per Point P Location Significance of P con figuration. In previous studies, the Green’s function method has been compared with results from sophisticated numerical models and found to produce unbiased results within 2 °C standard deviance or 2 % of maximum value, provided that P is chosen in the appropriate domain of application (see above) and that the thermal properties of the host rock formation are homogeneous in space [Myers et al. 2015; Heierli 2016]. Results The evolution of temperature at decision points P 1 and P 2 (Figure 1a, Table 2) has been calculated for the baseline configuration C a in argillaceous rock, as well as for a number of parameter variations thereof. The results for u(t,P 1 ; C a ) and for u(t,P 2 ; C a ) are presented in Figures 2 and 3 respectively. The same procedure was applied for decision point P 3 in con figuration C b for crystalline rock (Figure 1b, Table 2). Corresponding results for u(t,P 3 ; C b ) are presented in Figure 4. The y-axis in the graphs designates the change in temperature at P i . In order to obtain the resulting temperature, the local undisturbed temperature has to be added (this is approximately 38 °C in 650 m depth in Figure 2 and 37 °C in 630 m depth in Figure 3). In panels a to f, one and only one engineering parameter has been changed with respect to the baseline configuration. Panel g shows the temperature for both the baseline configuration and alternative configurations with three parameters changed simultaneously, leading to a lower and shorter temperature peak. The uppermost curves in every panel are identical and represent the temperature evolution in the baseline configuration. The dashed curves represent asymptotic limits. The arrows indicate the path of the temperature peak under variation of one parameter, e.g. cooling time in panel a. The arrows points towards increasing technical effort. Discussion In the baseline configuration C a for argillaceous rock, the temperature P 1 P 0 + (x = 0, y = 1.50, z = 0 ) Retrievabilty, degradation of backfill material. P 2 P 0 + (0, 0. 20.0) Pore water pressure P 3 P 0 + (0, 0.88, 0) Retrievability, degradation of bentonite. | | Tab. 1. Location of decision points P i relative to the midpoint P 0 of a central batch. The x-axis is taken parallel to the drift axis, the y-axis perpendicular to x in the plane of the repository and the z-axis is taken perpendicular to the repository plane. DECOMMISSIONING AND WASTE MANAGEMENT 321 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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