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Modeling the Effect of Sorption Kinetics on Radionuclide Migration in Crystalline Rock
- Anders Wörman, Shulan Xu, Björn Dverstorp
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- Journal:
- MRS Online Proceedings Library Archive / Volume 506 / 1997
- Published online by Cambridge University Press:
- 10 February 2011, 1089
- Print publication:
- 1997
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The preferred methods for nuclear waste disposal in Sweden are based on isolation in deep repositories in crystalline rock. As part of its research programme on the safety of final disposal, the Swedish Nuclear Power Inspectorate (SKI) initiated a project to examine how spatial variability in rock chemistry in combination with spatial variability in matrix diffusion affects the radionuclide migration along single fractures in crystalline rock.
A mathematical framework describing migration was developed with a numerical simulation package. In order to determine statistical patterns in geochemistry, in-diffusion, through-diffusion, and batch experiments will be performed. The purpose is to use the knowledge of statistical patterns in geochemistry as a basis for stochastic predictions which will be validated against the results of several laboratory migration experiments.
A medium grained granite and a diorite were selected at Äspö hard rock laboratory in southeastern Sweden. Four drill cores with a diameter of 20 [cm] have been collected from each of two rock types. One of the four drill cores in each series was sliced into cubes in order to evaluate sorption characteristics, porosity and effective diffusivity by in-diffusion and through-diffusion experiments on the individual pieces. The other three drill cores are to be used in three migration experiments. Experiments with the two rock types are run in two parallel series. Currently, all the laboratory experiments are underway.
The present paper describes the mathematical framework used for planning and interpreting experimental results. In particular, the formulations for sorption kinetics and matrix diffusion are crucial for distinguishing between the effects of various hydrodynamic and geochemical effects. Neretnieks [I] proposed a one-dimensional formulation for radionuclide migration that includes the effect of matrix diffusion and instantaneous matrix sorption. This concept has been further developed into two dimensional formulations [2], [3]. The model framework developed in this project [4] includes additional first order sorption kinetics in the rock matrix. Preliminary analyses indicate that sorption kinetics (non-equilibrium sorption) are often sufficiently pronounced so as to significantly affect interpretation of other phenomena affecting the migration process. Acknowledgement of sorption kinetics is, therefore, deemed important for reliable generalisations of the retardation of radionuclide migration.
Several investigations of Cs sorption onto minerals indicate that equilibration time varies from weeks in laboratory tests with illite and montmorillonite [5] to up to several years under special conditions for Chernobyl Cs in lake sediments [6]. Comans et al., [7], Nyffeler et al., [8] and Smith and Comans [9] discussed the different equilibrium times associated with the readily available binding sites on grain surfaces and less available sites such as frayed edges or in the grain interior. Skagius [10] conducted experiments with adsorption and desorption of Cs on crushed granite in different size fractions, the major constituents of which were quartz, feldspar and microcline. In some experiments the ratio between dissolved and particulate phases of Cs was still changing even after more than a years time.
In order to quantify kinetics of Cs adsorption on granite batch tests were conducted on crushed rock. Relationships between surface area available to sorption and transfer rate coefficients, as well as the ratio of dissolved to adsorbed mass phase species at equilibrium are established from the experiments. The specific surface area for the parent, intact rock, as well as coefficients of sorption kinetics, can be evaluated by combining the results with the crushed rock with those of the parent intact rock. Hence the effect of sorption kinetics on the solute pulse propagation along a single fracture can be numerically simulated. The maximum concentration of the breakthrough from a Dirac mass spike is higher than that obtained with equilibrium sorption. The kinetics of the adsorption process during the uptake phase can be interpreted as a decrease in the effective partition coefficient (adsorbed/dissolved ratio). In contrast, sorption kinetics during the release phase, can be interpreted as the results of an increase in the partition coefficient. This, in turn, causes a prolonged tail in the breakthrough curve. If a Heaviside step function is used as a boundary condition, simulation indicates an earlier arrival of the breakthrough curve front than that obtained with equilibrium sorption.
The impact of sorption kinetics on breakthrough curves is of the same order as the effect of shear dispersion. This is of great importance in the interpretation of the migration tests and to future generalisations to a field scale.
Objectives and Limitations of Scientific Studies with Reference to the Swedish RD&D Programme 1992 for Handling and Final Disposal of Nuclear Waste
- Rolf Sjöblom, Björn Dverstorp, Stig Wingefors
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- Journal:
- MRS Online Proceedings Library Archive / Volume 333 / 1993
- Published online by Cambridge University Press:
- 25 February 2011, 209
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- 1993
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The Swedish Nuclear Power Inspectorate (SKI) has recently concluded its evaluation of the Swedish programme for the development of a system for the management of nuclear waste. The programme was compiled and issued by the Swedish Nuclear Fuel and Waste Management Company (SKB). In this process of programme formulation and review, considerable attention has been paid to the question of how scientific studies should be directed and performed in order to provide the support needed in the programme.
When the objectives and limitations of such scientific studies are to be analysed, it is vitally important that the implications of the long timescales and the lack of feedback of post-closure experience are fully understood and adequately dealt with. It must be realised, that simulations will have to be utilized for the systems development work as well as for the assessments of safety. Such performance simulations have to be based on a thorough understanding of the pertinent phenomena as well as on a comprehensive base of experimental data. They must also be based on a good overall perspective that can only be obtained through full performance assessments.
Thus, a sound scientific base is needed. The components of this base must be traceable. Moreover, the links must be clearly identified between the knowledge base and the development of the disposal system as well as the performance assessment of such a system. Performance simulations and performance assessments should be utilized, not only as tools to develop a system and to evalute its safety but also to identify areas where further research is required - or unnecessary.
The knowledge base will, however, always be limited, and a lack of understanding must also be recognised and adequately dealt with, e.g. by accounting for uncertainties in the performance simulations, by relying on bounding (conservative) assumptions or by robust repository design.
Thus, the success of a programme for the handling and disposal of nuclear waste is highly dependent on the strategy applied for the utilization of the scientific knowledge base. The requirements on such a strategy increase considerably when substantial commitments are to be made.
Modeling Flow and Transport in Fractured Crystalline Rock using the Discrete Fracture Network Concept
- Björn Dverstorp, Wille Nordqvist, Johan Andersson
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- Journal:
- MRS Online Proceedings Library Archive / Volume 127 / 1988
- Published online by Cambridge University Press:
- 26 February 2011, 787
- Print publication:
- 1988
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The conductive properties of fractured crystalline rock vary considerably in space, which implies that the flow is very unevenly distributed in space. The large variability raises doubts on modeling the flow with a large scale continuum model. Modeling flow in fractured crystalline rock in a network of discrete fractures provides an increased understanding of the character of the rock heterogeneity. Compared to a continuum model discrete models introduce new parameters such as statistical distributions for fracture orientation, radii, density and transmissivity that need to be estimated. By analyzing the migration experiment in the Stripa research mine in Sweden it is demonstrated how to calibrate and eventually validate a discrete model on field data. The flow analysis shows that the flow distribution on the drift roof and in two out of three vertical boreholes can be modelled with the same discrete model. The properties of the third borehole differ substantially. Initial attempts of analyzing the tracer experiment are also described.