An inverse method predicting thermal fluxes in nuclear waste glass canisters during vitrification and cooling

Abstract

We report a method to model, simulate and predict high-level nuclear waste (HLW) thermal behavior over short and long time-scales. The approach relies on an inverse method using homogenized thermal fluxes at the HLW package surfaces during the vitrification process. The thermal simulation can then be used as input in subsequent structural analyses. This allows us to compare for two different vitrification processes the developed thermal stress build-up investigated inside the glass block. The first process is the original experimental vitrification process, without the presence of the radionuclides. The second one is a simulation made possible by the proposed inverse method, where the cooling and solidification for a HLW integrate the long-term heat source of the radionuclides.

Introduction

Disposing of ultimate nuclear wastes around the world remains challenging and has been considered with various possible strategies (Birac et al., 2002, Wealer et al., 2019). Lately in France, deep geological storage has received considerable attention, but the disposal of high-level nuclear waste (HLW) depends on available host bedrocks, also considering the type of stored waste products. The reference process currently in use for the management of such long-lived radionuclides is their vitrification as HLW packages (Bonniaud et al., 1980, Goel et al., 2019) that could be stored in a deep underground facility (see Acts 91–1381 of the 30 December 1991 and 2006–739 of the 28 June 2006; Andra, 2006, Andra, 2006, Andra, 2006, Andra, 2013, Wealer et al., 2019). Other similar vitrification facilities exist around the world (Decamps and Dujacquier, 1997, Gin et al., 2013, Gin et al., 2017, Vienna et al., 2013) leading to different processes developed to produce various kinds of HLW glasses (Goel et al., 2019, Perez et al., 2001, Tennant and Murphree, 1982). Different processes induce different thermal treatments that most significantly use different HLW glass block sizes. The resulting nuclear glasses have then specific thermal evolutions over several timescales, due to the accounting for the radionuclide decay rates. All such case-specific operational conditions make the following reported general approach adaptable to many kinds of vitrification, and very interesting to estimate the thermal response of HLW packages.

From the safety and environmental point of view, the manufacturing of these HLW packages induces internal cracking of the nuclear glass block during the vitrification and cooling processes, and their thermal treatments (Connelly et al., 2011, Faletti and Ethridge, 1988, Kahl et al., 1991, Peters and Slate, 1981, Riley et al., 1999). Hence, numerous studies were carried out on small glass samples such as (Doquet et al., 2013, Dubé et al., 2010, Mallet et al., 2013, Mallet et al., 2015, Ougier-Simonin et al., 2011, Perez and Westsik, 1981). Inside the glass matrix, the glassy phase transitions of the thermal expansion and the viscoelastic behaviors impact the thermal stress build-up for any of the relevant timescales. The behavior of the temperature gradients, thermal history and thermomechanical response of the HLW glass block can then be used to interpret trends of the vitrification process (Barth et al., 2012, Barth et al., 2014, Peters and Slate, 1981). Finally, the (thermo)mechanical response – using Continuum Damage Mechanics – can be calculated to predict and quantify relevant crack network developments of the glass block (Barth, 2013, Barth et al., 2015, Dubé et al., 2010).

When disposed under long-term underground storage conditions, the HLW packages’ exposure to water (leaching) also needs to be further investigated for confinement performance, which is particularly related to the internal cracking surface areas of the glass block (Gin, 2014, Riley et al., 1999, Schlegel et al., 2016, Seetharam et al., 2014). This alteration phenomenon was also studied using glass analogs (Frugier et al., 2008, Dillmann et al., 2016, Michelin et al., 2015, Parruzot, 2014, Verney-Carron, 2008). Another challenge lies at the repository scale with HLW thermal power influencing the lithostatic stresses and/or hydrogeological interactions with the repository (Cho et al., 2014, Kwon et al., 2013, Lee et al., 2014, Schneefuß et al., 1989, Seetharam et al., 2014, Tennant, 1982, Urpi et al., 2019). It should be noted that thermally activated nuclear glass crack may heal by mechanical loadings (Doquet et al., 2015), and that also other complementary effects on materials properties are linked to the radioactivity (Gin, 2014, Gin et al., 2017). At the larger scale, the repository configurations engineered with designed confinement structures, e.g. for a large number of HLW packages, need to be accounted for integrating all these important phenomena. By parts, depending on the multi-physics approach developed, this is abundantly reported in the literature so to evaluate ultimately the safety of underground repositories (Andra, 2006, Avila et al., 2000, Cha et al., 2017, Hodgkinson, 1980, Hodgkinson and Bourke, 1980, Kar et al., 2008, Li et al., 2009, Li et al., 2011, Moncouyoux and Jacquet-Francillon, 1993, Sizgek, 2005).

As a result, a complete dimensional and temporal multi-scale approach of thermal, mechanical and leaching phenomena would help in the prediction of the capacity of any HLW repositories to comply with given environmental standards. A combining effort towards such aim was proposed by the computational approaches of Bouyer and coworkers (Crevoisier et al., 2011, Repina et al., 2019, Repina et al., 2020). However, most of the aforementioned thermal studies only deal with the HLW as a thermal source term, depending on the radionuclides mix. This is often the case as a point source or linked to the geometry approximation of the package (Bulut Acar and Zabunoğlu, 2013, Finsterle et al., 2019). In such configurations, the HLW packages with thermal power to dissipate due to the presence of radioactive waste are in thermal balance with their direct environment. In fine, the thermal history of each HLW package has an effect on the ultimate internal structure of the HLW glass block. The track of this thermal history stems from the cast and cooling process conditions, to the temporary storing conditions, and finally to the ongoing repository characteristics (its design and the neighboring rock formation). Hence, to better predict the ultimate internal structure of the HLW glass blocks, better tools and knowledge of the HLW packages’ thermal history need to be exploited.

The aforementioned reported studies cover multi-physics approaches contributing by part to address the ultimate metric of the confinement of radionuclides. With the nature of the thermo-mechanical response of the HLW glass block, the crack network is the result of the thermal history of this glass structure. Mechanical loadings may further damage the thermally-induced crack network, under repository conditions or at the occasion of mishandlings. In this context, a predictive tool to determine the thermal history of each glass block is relevant over timescales corresponding to the cooling process, i.e. to the glass solidification and to the cooling end after tens or even hundreds of thousands of years.

To this aim, we present a numerical approach, which is applicable to any HLW vitrification process. The purpose of the proposed tool is to more accurately predict the global thermal kinetics of the nuclear glass by imposing thermal fluxes corresponding to the process used over short and long periods of time as compared to only known external temperatures for a given process at the can surfaces. We model the thermal behavior using an inverse thermal method within the glass block during the complete vitrification process. This is carried out by considering the nuclear glass composite as a homogeneous media for the thermal conduction, during its cooling periods (short and long), even encompassing the integration of the cracking phenomena after solidification.