IntroductionWorldwide, there are three high-level nuclear waste repositories under construction. Both the Forsmark granite project in Sweden and the Olkiluoto granite project in Finland are in an advanced stage of licensing. These two projects (SKB 2006; POSIVA 2006) and the former Columbia River Basalt (CRB) project in the USA (Lutton et al. 1986) envisage the storage of waste in copper-shielded steel containers surrounded by a bentonite buffer. The Opalinus Clay project in Switzerland has the option of both copper-shielded containers and unshielded containers (HSK 2005). The Bure clay project in France is in an early stage of licensing. The design of this project is exceptional in that it exclusively considers unshielded steel containers implying very high corrosion rates (ANDRA 2016). However, the final design may change in the course of the licensing procedure.Copper-shielded waste containers are the optimal solution, and there is hardly any room for improvement in the general container design and emplacement method (KBS-3V disposal concept; SKB 2006; POSIVA 2006). However, the search for the optimal mineralogical composition of the bentonite buffer surrounding the container (NDA 2014; POSIVA 2017) has not been completed yet. This is shown by the Forsmark project, which is one of the two projects in the advanced stage of licensing. In a nutshell, the applicant (SKB) claims that sulfur was not the main corrosion agent for copper in a 20-year corrosion experiment with copper embedded in MX-80 bentonite, which has a relatively high calcium sulfate content (1.3%; Carlson 2004). The licensing authority SSM has considerable doubts in this respect and has been looking for advice from consultants even up to early 2021 (MKG 2021).Prior to 2006, MX-80 bentonite had been the only reference buffer material in the KBS-3V disposal concept (NDA 2014). In 2006, SKB initiated the Alternative Buffer Material project with 10 additional materials (Eng et al. 2007; Svensson et al. 2011); these materials have a calcium sulfate content above and below that of the MX-80 bentonite.The mineralogy exerts a nonnegligible influence on the corrosion rate of the copper shield, especially with respect to sulfate mineral concentration. The objective of this paper is the quantification of the buffer-dependent corrosion rates of the copper shield.MethodThe structured orthogonal model mesh contains 36 elements and has dimensions of 1 × 1 × 0.36 m (Table 2). The mesh represents the standard design for nuclear waste disposal (SKB 2006; POSIVA 2006) with the host rock (first node) and the 35-cm-thick bentonite buffer (intermediate nodes) placed adjacently to the 5-cm-thick copper shield (last node). Except for the first node, the cell volume of the individual elements is 0.01 m3. The first element has a volume of 1052 m3, which imposes Dirichlet conditions, that is, the thermodynamic conditions of this element do not change at all.Table 2. Model setupParameterDimensionValueSimulation perioda106Model length/width/heightcm36/100/100Temperature°C25PressureMPa0.1Porosity—0.4Permeabilitym210−20Diffusion coefficient (all species)m2/s7 × 10−12The transport conditions are simulated with the thermodynamic data of the EQ3/6 V8b.2 database (TherAkin10.dat; Wolery 1992), which were derived using SUPCRT92 (Johnson et al. 1992), supplemented with the thermodynamic data for the solid-phase lepidocrocite (Majzlan et al. 2003a, b) and the liquid species CuCl° and CuCl− (Xiao et al. 1998). All liquid species in the database are allowed to take part in the reactions, the total comprising 128 liquid species. The solid phases react under kinetic constraints, with precipitation rates equal to dissolution rates. The rate constants are taken from Palandri and Kharaka (2004), except for native copper and chalcocite (Table 3). The rate constant for native copper (4.195 × 10−10 mol m−2 s−1) is calculated from a general corrosion rate of 9.4 × 10−7 m/a (King 2009). The rate constant for chalcocite is set equal to the rate constant for native copper.Table 3. TOUGHREACT flow-transport model setup: initial volume fractions, reactive surface areas, and kinetic propertiesTable 3. TOUGHREACT flow-transport model setup: initial volume fractions, reactive surface areas, and kinetic propertiesMineralChemical composition
Initial volume fractionReactive surface area (m2/m3)k25 (mol/m2/s)bEa (kJ/mol)bn(H+)bk25 (mol/m2/s)Ea (kJ/mol)k25 (mol/m2/s)Ea (kJ/mol)n(H+)CalciteCaCO30.03,2005.01 × 10− × 10−623.53.31 × 10−435.41.00QuartzSiO20.02,800———1.03 × 10−1487.7———GypsumCaSO4 · 2H2O0.0–0.0073,200———1.62 × 10−303.89 × 10−1548.0−0.13AnhydriteCaSO40.0–0.0073,200———6.46 × 10−414.3———HematiteFe2O30.0–0.0074,6004.08 × 10−1062.21.002.52 × 10−1566.2———GoethiteFeOOH0.0–0.0074,600———1.50 × 10−886.5———LepidocrociteFeOOH0.0–0.0074,600———1.50 × 10−886.5———PyriteFeS20.05,4003.02 × 10−856.9−0.52.82 × 10−1056.9———Native copperCu0.0–0.9540———4.195 × 10−10————ChalcociteCu2S0.0540———4.195 × 10−10————Na-smectiteNa0.29Al1.77Mg0.26Si4O10(OH)20.0–0.924,0001.05 × 10−1123.60.341.66 × 10−1335.03.02 × 10−1758.9−0.40K-smectiteK0.29Al1.77Mg0.26Si4O10(OH)20.024,0001.05 × 10−1123.60.341.66 × 10−1335.03.02 × 10−1758.9−0.40Ca-smectiteCa0.145Al1.77Mg0.26Si4O10(OH)20.024,0001.05 × 10−1123.60.341.66 × 10−1335.03.02 × 10−1758.9−0.40The reactive surface area of smectite is that of Friedland bentonite (Karnland 2010). The remaining values are taken from a TOUHGHREACT test case (Xu et al. 2014), whereby the value for anhydrite is used for calcite and gypsum, the value for goethite is used for hematite and lepidocrocite, and native copper and chalcocite use the surface area of pyrite multiplied by 0.1. All minerals are allowed to precipitate and dissolve.In the first cell, which is subjected to Dirichlet conditions, the initial volume fraction is zero for all minerals. The intermediate cells (No. 2-35) representing the bentonite buffer initially have 90% Na-smectite or 90% Na-smectite and accessory minerals, depending on the model setup according to the composition of common candidate buffer materials (Table 4):
•0.7% hematite (Fe2O3),•0.7% goethite (α-FeOOH),•0.7% lepidocrocite (γ-FeOOH),•0.7% gypsum (CaSO4 · 2H2O),•0.7% anhydrite (CaSO4), and•the combination of an iron oxide and calcium sulfate, for example, 0.7% hematite + 0.7% gypsum.Table 4. Mineralogical and chemical characterization of bentonites, which are candidate buffer materials for nuclear waste disposalTable 4. Mineralogical and chemical characterization of bentonites, which are candidate buffer materials for nuclear waste disposalBentoniteCountryChemical analysis S (%)ReferenceCalcium sulfate (gypsum) (anhydrite) (%)Hematite (%)Fe oxyhydroxide (goethite) (lepidocrocite) fcc (%)StranceCzech Republic——10–15<0.1Carlson (2004)MX-80USA1.3——0.31Carlson (2004)BH-200USA2.9——0.69Carlson (2004)FriedlandGermany0.1–1.20–0.70.1–1.40.5Karnland et al. (2006)KutchIndia0.3–2.20–0.81.1–1.60–0.1Karnland et al. (2006)AvonsealCanada2——0.4Quigley (1984)AvongelCanada3——0.6Quigley (1984)FiltaclayCanada3——0.6Quigley (1984)DeponitGreece1.8——SKB (2006)The remaining minerals are native copper, chalcocite, pyrite, Ca-smectite, K-smectite, calcite, and quartz, which all have an initial volume of zero.The last cell (No. 36) representing the copper shield initially has 90% native copper and 3% Na-smectite with additional components equal to those of the intermediate cells (No. 2-35). The initial fluid composition in all cells is that of each individual reference groundwater. The liquid flow is zero between all cells. The transport of liquid species occurs by diffusion only. The TOUGHREACT code calculates reactive transport with a single global diffusion coefficient. Because HS− is the most important corrosion rate-determining species, the global diffusion coefficient is set equal to that of HS− (7 × 10−12 m2 s−1; King et al. 2002). The simulation period is 1 million years.ResultsAll simulations showed a satisfactory convergence behavior, except for two sets of simulations with accessory anhydrite (Forsmark and Olkiluoto groundwater). In the remaining 47 models, the general corrosion depth of the 5-cm-thick native copper (Cu°) shield at the end of the 1-million-year simulation period is in the range of 0.002–0.08 cm (Fig. 1).The groundwater composition has a relatively strong influence on the corrosion depth, whereby a groundwater composition corresponding to a relatively short distance from the Cu°–chalcocite (Cu2S) boundary in the Eh–pH space of the Cu–S–Cl–O–H system [Fig. 2(a)] allows relatively little corrosion. The minimum corrosion depth (0.002 cm) is recorded for the CRB test case, which represents a groundwater composition with a relatively small distance from the Cu°–Cu2S boundary. The maximum corrosion depth (0.08 cm) is recorded for the Forsmark test case, which represents a relatively large distance from the Cu°–Cu2S boundary. The remaining three test cases occupy an intermediate position both in terms of the Cu° corrosion depth and in terms of distance from the Cu°–Cu2S boundary.The influence of bentonite composition is weaker than that of groundwater composition but, nevertheless, significant. The calcium sulfate-bearing buffer has a corrosion depth that is a maximum eight times greater than that recorded for a buffer without calcium sulfates.DiscussionThe general corrosion depth of native copper (Cu°) that is determined with the reactive-transport model in this paper only considers the low-Eh side of the Cu° stability field (Fig. 2). Nevertheless, the high-Eh side may be relevant for groundwater with an especially low Cu/Cl activity ratio. The five reference groundwaters used in this study are shallow groundwaters with a relatively high Cu/Cl activity ratio. However, deeper groundwaters that have equivalent Cu concentrations but inevitably have a higher salinity (thus, lower Cu/Cl activity ratios) may be under consideration in other disposal projects. Fortunately, there is a simple technical solution that alleviates the problem of low Cu/Cl groundwaters. Wang and Hadgu (2020) propose to embed 1% copper wires or meshes in the bentonite buffer albeit for a different reason (heat dissipation). The side benefit of such a design will be an enhanced Cu/Cl activity ratio in the interstitial water of the bentonite buffer, because some copper of the wires or mesh dissolves; thus, the Cu/Cl activity ratio of the fluid reaching the copper shell of the waste container is relatively high. Note that low Cu/Cl groundwater, which will justify the modified design for purely chemical reasons, is not modeled in this paper, because there are no real-world examples available that can show that the high-Eh side of the Cu° stability field is critical.On the low-Eh side, the Cu° corrosion depth that is determined with the reactive-transport model in this paper tends to be lower than that of previous nonreactive transport models. Previous calculations predict a general corrosion depth of 0.04–0.1 cm at the end of a 1-million-year simulation period for Scandinavian and North American sites (Schwartz 2008, 2018, 2019), whereas the new values range from 0.002 to 0.08 cm. The general corrosion depth has to be multiplied by a correction factor to obtain the actual value for pit corrosion. King et al. (2002) estimate that the correction factor is in the range of 5 (realistic value) to 25 (conservative value). 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