Jan-Olof Selroos

Comparison of alternative modelling approaches for groundwater flow in fractured rock

In performance assessment studies of radioactive waste disposal in crystalline rocks, one source of uncertainty is the appropriateness of conceptual models of the physical processes contributing to the potential transport of radionuclides. The Alternative Models Project (AMP) evaluates the uncertainty of models of groundwater flow, an uncertainty that arises from alternative conceptualisations of groundwater movement in fractured media. The AMP considers three modelling approaches for simulating flow and advective transport from the waste canisters to the biosphere: Stochastic Continuum, Discrete Fracture Network, and Channel Network. Each approach addresses spatial variability via Monte Carlo simulation, whose realisations are summarised by the statistics of three simplified measures of geosphere performance: travel time, transport resistance (a function of travel distance, flow-wetted surface per volume of rock, and Darcy velocity along a flowpath), and canister flux (Darcy velocity at repository depth). The AMP uses a common reference case defined by a specific model domain, boundary conditions, and layout of a hypothetical repository, with a consistent set of summary statistics to facilitate the comparison of the three approaches. The three modelling approaches predict similar median travel times and median canister fluxes, but dissimilar variability. The three modelling approaches also predict similar values for minimum travel time and maximum canister flux, and predict similar locations for particles exiting the geosphere. The results suggest that the problem specifications (i.e. boundary conditions and gross hydrogeology) constrain the flow modelling, limiting the impact of this conceptual uncertainty on performance assessment.

Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport

[1]xa0Velocity distributions in two- and three-dimensional networks of discrete fractures are studied through numerical simulations. The distribution of 1/v, where v is the velocity along particle trajectories, is closely approximated by a power law (Pareto) distribution over a wide range of velocities. For the conditions studied, the power law exponents are in the range 1.1–1.8, and generally increase with increasing fracture density. The same is true for the quantity 1/bv, which is related to retention properties of the rock; b is the fracture half-aperture. Using a stochastic Lagrangian methodology and statistical limit theorems applicable to power-law variables, it is shown that the distributions of residence times for conservative and reacting tracers are related to one-sided stable distributions. These results are incompatible with the classical advection dispersion equation and underscore the need for alternative modeling approaches.

Hydrodynamic control of tracer retention in heterogeneous rock fractures

[1]xa0We investigate the statistical properties of a Lagrangian random variable β [T/L], which has been shown to quantify hydrodynamic impact on retention [Cvetkovic et al., 1999], using Monte Carlo simulations of flow and transport in a single fracture. The “local cubic law” of water flow is generalized to a power law Q ∼ bn, where Q is the flow rate, b is the half aperture, and n ≤ 3. Simulations of flow and particle transport are carried out assuming “local cubic law” (n = 3) and “local quadratic law” (n = 2), and for two typical flow configurations: uniform flow and radially converging flow. We find that β is related to τ as β ∼ τm, where m is dependent on the power n and the configuration of flow and transport. Simulation results for uniform flow indicate that for a small source section; as the source section increases, we have the convergence to β ∼ τ. For radially converging flow, we find β ∼ τ for a small source section and a convergence to β = const for an increasing source section. Simulation results for both flow configurations are consistent with the results for a homogeneous fracture. The results for a homogeneous fracture provide reasonable bounds for simulated β. The correlation between β and Q is relatively weak for all cases studied.

Comparative measures of radionuclide containment in the crystalline geosphere

Abstract A probabilistic model for assessing the capacity of a fractured crystalline rock volume to contain radionuclides is developed. The rock volume is viewed as a network of discrete fractures through which radionuclides are transported by flowing water. Diffusive mass transfer between the open fractures and the stagnant water in the pore space of the rock matrix allow radionuclides access to mineral grains where physical and chemical processes—collectively known as sorption—can retain radionuclides. A stochastic Lagrangian framework is adopted to compute the probability that a radionuclide particle will be retained by the rock, i.e., the probability that it will decay before being released from the rock volume. A dimensionless quantity referred to as the “containment index” is related to this probability and proposed as a suitable measure for comparing different rock volumes; such a comparative measure may be needed, for example, in a site selection program for geological radioactive waste disposal. The probabilistic solution of the transport problem is based on the statistics of two Lagrangian variables: τ, the travel time of an imaginary tracer moving with the flowing water, and β, a suitably normalized surface area available for retention. Statistics of τ and β may be computed numerically using site-specific discrete fracture network simulations. Fracture data from the well-characterized Äspö Hard Rock Laboratory site in southern Sweden are used to illustrate the implementation of the proposed containment index for six radionuclides (126Sn, 129I, 135Cs, 237Np, 239Pu, and 79Se). It is found that fractures of small aperture imply prolonged travel times and hence long tails in both beta and tau. This, in turn, enhances retention and is favorable from a safety assessment perspective.

Overview of hydrogeological safety assessment modeling conducted for the proposed high-level nuclear waste repository site at Forsmark, Sweden

Nuclear energy production is dependent on safe long-term management of the spent nuclear fuel resulting from the operation of the power plants. Thus, the realization and societal acceptance of final subsurface repositories for highlevel nuclear waste, so-called ‘geological disposal’, which will isolate the waste for an extended period of time, are of utmost importance to future nuclear energy production. The process of siting and obtaining permission to operate a repository for nuclear waste disposal is typically a long and complex process. In Sweden, the Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the handling and final disposal of all nuclear waste. During the last three decades, SKB has made progress both in terms of developing a repository concept and in investigating several sites. The Swedish program for geological disposal of spent nuclear fuel is at a major milestone in the form of recently submitted permit applications for the construction of an encapsulation plant and a final repository. The concept developed for geological disposal is denoted ‘KBS-3’ and consists of copper canisters deposited in vertical deposition holes under the floor of deposition tunnels located at approximately 500 m depth in crystalline bedrock (SKB 1983; Banwart et al. 1997; Hedin et al. 2001; Thegerström and Olsson 2011). The canisters have a cast-iron insert to provide mechanical stability, and are surrounded by bentonite clay in the deposition hole. The tunnels are backfilled and pumping that has been draining the tunnels stops; thereafter, groundwater begins to resaturate the repository. TheKBS-3 system is, thus, a multi-barrier system where the three independent barriers are the copper canister, the bentonite buffer, and the bedrock. The siting process in Sweden has been performed using a staged approach resulting in present plans to construct a repository for spent nuclear fuel at the Forsmark site on the Swedish east coast (Fig. 1a). The siting process started in the late 1970s and early 1980s when twelve so-called study sites in the Fennoscandian Shield with different geological settings were investigated geoscientifically, including a few boreholes down to approximately 700 m depth (Fig. 1b). This was followed in the 1990s by so-called feasibility studies where eight municipalities were assessed not only from a geoscientific viewpoint but also from environmental and societal viewpoints using all available data at hand (Fig. 1c). The municipalities involved in the feasibility studies first approved the feasibility study and later decided whether they wanted to be part of the continued process. In the early 2000s, two sites were chosen and accepted for detailed site investigations, the Forsmark site in the municipality of Östhammar and the Laxemar-Simpevarp site in the municipality of Oskarshamn (Fig. 1c). The site investigations were carried out during the period 2002– 2008 and included airborne investigations and surfacebased methods including drilling to a maximum vertical depth of approximately 1 km. A total of 20–40 deep cored-drilled boreholes were drilled at each site. Parallel to the site investigations, site-descriptive modeling was performed. The aim of the site-descriptivemodelingwas to develop a discipline-integrated account of the past and present conditions at the site by analyzing, assessing, and modeling the data obtained during the characterization. The site-descriptive model constitutes an integrated description of the site and its regional setting, including the current state of the geosphere and the biosphere as well as natural processes affecting long-term evolution. The site description is intended to serve the needs of both high-level nuclear-waste repository engineering with respect to layout and construction, and of safety assessment with respect to long-term performance. It also provided a basis for the environmental impact assessment. Received: 15 November 2012 /Accepted: 7 November 2013 Published online: 15 December 2013

SR 97: Post-Closure Safety for a KBS 3 Deep Repository for Spent Nuclear Fuel - Overview -

In preparation for coming site investigations for siting of a deep repository for spent nuclear fuel, the Swedish Nuclear Fuel and Waste Management Company, SKB has carried out the long- term safety assessment SR 97, requested by the Swedish Government. The repository is of the KBS-3 type, where the fuel is placed in isolating copper canisters with a high-strength cast iron insert. The canisters are surrounded by bentonite clay in individual deposition holes at a depth of 500 m in granitic bedrock. Geological data are taken from three sites in Sweden to shed light on different conditions in Swedish granitic bedrock. The future evolution of the repository system is analyzed in the form of five scenarios. The first is a base scenario where the repository is postulated to be built entirely according to specifications and where present-day conditions in the surroundings, including climate, persist. The four other scenarios show the evolution if the repository contains a few initially defective canisters, in the event of climate change, in the event of earthquakes, and in the event of future inadvertent human intrusion. The principal conclusion of the assessment is that the prospects of building a safe deep repository for spent nuclear fuel in Swedish granitic bedrock are very good. The results of the assessment also serve as a basis for formulating requirements and preferences regarding the bedrock in site investigations, for designing a program for site investigations, for formulating functional requirements on the repositorys barriers, and for prioritization of research.

Microtomography-based Inter-Granular Network for the simulation of radionuclide diffusion and sorption in a granitic rock

Field investigation studies, conducted in the context of safety analyses of deep geological repositories for nuclear waste, have pointed out that in fractured crystalline rocks sorbing radionuclides can diffuse surprisingly long distances deep into the intact rock matrix; i.e. much longer distances than those predicted by reactive transport models based on a homogeneous description of the properties of the rock matrix. Here, we focus on cesium diffusion and use detailed micro characterisation data, based on micro computed tomography, along with a grain-scale Inter-Granular Network model, to offer a plausible explanation for the anomalously long cesium penetration profiles observed in these in-situ experiments. The sparse distribution of chemically reactive grains (i.e. grains belonging to sorbing mineral phases) is shown to have a strong control on the diffusive patterns of sorbing radionuclides. The computed penetration profiles of cesium agree well with an analytical model based on two parallel diffusive pathways. This agreement, along with visual inspection of the spatial distribution of cesium concentration, indicates that for sorbing radionuclides the medium indeed behaves as a composite system, with most of the mass being retained close to the injection boundary and a non-negligible part diffusing faster along preferential diffusive pathways.