A Methodology to Evaluate the Diffusion Coefficient of Radionuclides through Rock Mass in a Short Experimental Duration

Geological isolation of nuclear waste requires laboratory and field investigations to evaluate migration parameters such as diffusion and dispersion coefficient of radionuclides in order to assess the site suitability for locating a high level radioactive waste repository. However, migration of radionuclides through the rock mass away from the radioactive waste repository is an extremely slow process and the laboratory experiments to evaluate the diffusion coeffficient (Di) of radionuclides are time consuming. The present study deals with the development of a methodology adopting a centrifuge modeling technique to evaluate the diffusion coefficient of radionuclides through the fractured and the intact rock mass over a very short experimental duration. This is achieved by simulating the diffusion of Iodide, Cesium and Strontium ions through sliced rock samples in a specially designed diffusion cells under a high gravitational field in a Geotechnical Centrifuge. Results indicate that the diffusion time of these ions through the rock mass in the centrifuge is reduced by N times compared with conventional laboratory diffusion tests, where the N is the applied ‘g’ (acceleration due to gravity). Di of I, Cs and Sr through the fractured and intact rock samples is found to range from 0.60 to 8.3×10m/s and 1.2 to 4.9×10 m/s, respectively. Evaluating migration parameters rapidly helps to simulate the in-situ conditions needed to study the long term effect of radionuclide migration in geo-environment. INTRODUCTION Isolation of nuclear waste in deep geological formations is considered worldwide as the suitable option to protect man and the environment for extended periods. In a deep geological repository migration of waste components away from the disposal site mainly depends on the physical condition of the rock mass, the type of the minerals present in it and their reactivity with the various radionuclides (sorbing or non-sorbing) released from the waste [1]. Mechanisms which control the contaminant migration through the rock mass are advection and/or diffusion [2]. To understand these mechanisms conventional laboratory experiments are conducted [3,4] and the results are used for the development and validation of theoretical models to predict the long-term behaviour of radionuclides. The interaction between various geometrical factors (such as WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001 fundamental properties/characteristics of the porous medium, fractured porous medium) and several other physico-chemical processes (such as retardation, matrix diffusion, particle transport, dispersion) result in a distribution of radionuclide between the solid and the liquid phase in the geo-environment. Other factors are related to the nature of the aqueous phase and the dissolved radionuclides [5]. This necessitates a thorough understanding of the waste-geoenvironment interaction for selection of a suitable disposal site. The laboratory experiments are quite time consuming and cost intensive. At the same time, these experiments suffer from the limitations associated with the incorporation of material complexity, difficulty associated with reproduction of the boundary conditions, which control the governing mechanism(s) and differences in the time scales for completion of the processes [6]. At the same time, theoretical models developed based on laboratory and field experiments lack validation due to mismatch of time scale and uncertainties associated with long-term predictions to demonstrate the safety of deep disposal options [7]. In this context, several researchers [8,9,10] have recently demonstrated the usefulness of Centrifuge modeling techniques to simulate the naturally slow processes of contaminant migration in soil mass in a short duration of time. These researchers have also derived the scaling factors for the modeling purpose. Villar and Merrifield [11,12] have simulated the fate and behavior of disposed radioactive waste, through sands, under the conditions prevailing in a deep geological repository. These studies help in development of an improved conceptual understanding of contaminant transport mechanisms. However, the centrifuge modeling technique has not been extended to study and simulate contaminant migration through the rock mass. Realizing the fact that the contaminant migration through the rock mass is an extremely slow process, an attempt has been made in this paper to demonstrate the feasibility of the centrifuge modeling technique to model the contaminant diffusion through intact and fractured rock mass in the absence of other migration mechanisms like advection, dispersion etc. With this in view, a methodology has been developed to evaluate the diffusion coefficient of various waste components over a very short experimental duration. This has been achieved by simulating the diffusion of Cesium, Strontium and Iodide ions through intact and fractured rock masses in specially designed diffusion cells in a geotechnical centrifuge. Diffusion coefficients of these ions thus estimated are validated vis-à-vis those reported by the earlier researchers. CENTRIFUGE MODELING Centrifuge modeling is emerging as a useful technique to study and model various geoenvironmental problems [6]. The technique is here extended to study diffusion of contaminants through the rock mass. In a centrifuge, the rock sample (model) experiences the same magnitude and distribution of self-weight stresses as those of its prototype. The main difference between the model and its prototype is that the linear dimensions of the prototype are scaled down by a factor of N, at centrifugal acceleration N times greater than g, the acceleration due to Earth’s gravity. However, the model in the centrifuge has a free unstressed upper surface and within the sample the magnitude of stress increases with depth at a rate related to the sample density and strength of the acceleration field, N.g. WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001 During operation of the geotechnical centrifuge, g along the length of the model is different due to the linear variation of the acceleration, (ω.r), where ω is the angular velocity and r is the (effective) radial distance of an element in the model, from the axis of rotation, and can be obtained by using the following equation [13]: 3 h r r m t+ = (Eq. 1) where rt is the radial distance to the top of the model and hm is the length of the model. In the present study, a small geotechnical centrifuge, with the details presented in Table I, has been employed. However, to overcome various shortcomings associated with the small centrifuge and a small size model, a big centrifuge must be used. This would enable to some extent the incorporation of inherent material heterogeneity as well as anisotropy. At the same time, the transport mechanisms occurring in the model under controlled boundary and initial conditions may also be used to verify and improve the capabilities and efficiency of various mathematical and analytical models used for predicting the transport mechanisms involved in the geoenvironment. However to predict the prototype behaviour correctly, from the observed model behaviour, similar conditions must be established for the model and the prototype [8,10]. Table I Centrifuge details Type Swinging buckets on both sides of the arm Arm radius 200 mm Max. outer radius 315 mm RPM range 250-1000 Max. acceleration 300 g Capacity 0.72 g tons Spin-up time 20 s Spin-down time 80 s Scaling laws for contaminant transport through porous media. Arulanandan et al. [8], Hensley and Schofield [9] have derived scaling laws that govern the relationship between the centrifuge model and its prototype for contaminant migration through soils. For the sake of completeness, the summary of the scaling relationships is presented in Table II. Table II Scaling factors for centrifuge modeling Parameter Model scale Length 1/N Pore size 1 Porosity 1 Stress 1 Strain 1 Mass 1/N Mass density 1 Time (diffusion) 1/N WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001 Scaling of the diffusion process and time For a problem where advection, diffusion, dispersion and adsorption occur, the physical properties that define the concentration, C, of a contaminant may be given by: C= f (μ, Di, s, vs, σ, ρ, g, l, d, t, bulk soil properties) (Eq. 2) where C is the concentration of the contaminant, μ is the dynamic viscosity of the fluid; Di is the coefficient of molecular diffusion, s is the mass of adsorbed contaminant per unit-volume, vs is the interstitial flow velocity, σ is the surface tension for fluid/particle interface, ρ is the density of the fluid, g is the acceleration due to the gravity, l is the characteristic macroscopic length (the sample thickness), d is the characteristic microscopic length (particle size), and t is the time. The Coefficient of diffusion for an ion in the porous media is a function of both the medium and the free diffusion coefficient of the ion in the solution. For the same radionuclide and an identical rock mass, subjected to similar stress in the model and its prototype, the condition (Di)m = (Di)p, where subscripts m and p indicate model and prototype, respectively, should result. To maintain the ratio (Di.t/l) invariant, the condition tp=N.tm must be met. Scaling of linear dimensions If the sample used for the model and its prototype is identical and the model is subjected to higher acceleration, in a spinning centrifuge, the vertical stress at a depth hm, in the model, will be identical to that in the corresponding prototype at depth hp. As such, for the rock sample of density, ρ, the vertical stress, σm, at a depth, hm, in the model can be represented as: σm = ρ.N.g.hm (Eq. 3) Similarly, for the same sample, the vertical stress σp, at a depth, hp, in the prototype would be: σp = ρ.g.hp (Eq. 4) As such, for σm to be same as σp: hm = hp.N (Eq. 5) As per Eq. 5 the scale factor (model to prototype) for the linear dimensions is 1/N. The equation states that stress similarity is achieved at homologous points in the model and its prototype by accelerating a model of scale 1/N to N times Earth's gravity. Since the model is a linear scale representation of the prototype, the same scale factor may be imposed to displacements also. It therefore follows that strain scales to a factor of 1. As such, the sample stress-strain properties of the model are identical to that of the prototype. WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001 EXPERIMENTAL INVESTIGATIONS Rock cores used in the present study have been collected from the deep boreholes drilled in the Charnockite rock formation of Kalpakkam, India. The mineralogical and chemical composition, and physical and mechanical properties of the rock samples are presented in Table III [14] and Table IV [15], respectively. Table III Mineralogical and chemical composition of the rock samples Mineral Modal percent Oxide % by weight Quartz K-feldspar Plagioclase Biotite Apatite Opaques Hypersthene Garnet Pyroxene 35.8 20.8 16.4 7.5 2.2 4.1 --10.0 3.2 SiO2 Al2O3 Fe2O3 FeO MnO CaO MgO Na2O K2O TiO2 P2O5 LOI 63.06 6.59 0.79 5.55 0.05 3.16 2.96 3.66 2.51 0.75 0.46 0.46 Table IV Physical and mechanical properties of the rock samples Parameter Value Total porosity (%) 0.32 Water absorption (%) 0.22 Young’s modulus (GPa) 95 Poisson’s ratio 0.22 Uni-axial Compressive Strength (MPa) 161 Bulk density (g/cc) 2.58 These cores are sliced into the required thickness for conducting prototype (1-g tests) and centrifuge (N-g tests) diffusion tests. The slicing is done using high-speed rock cutting machine. These slices are polished, with the help of rock polishing machine, and their surface is cleaned using an ultrasonic surface cleaner. These rock slices were soaked in water for about four months before conducting experiments. The thicknesses of the samples chosen for the diffusion through intact and fractured rock slices are 3mm and 60mm respectively. Using a rock core splitter, a fracture along the rock core axis has been created in the 60mm thick samples and the fracture aperture is determined using a microscope after fixing it in the experimental set up. To ensure no leakage of the source solution in the measuring compartment, the sides of the rock sample have been sealed using silicone adhesive. The fracture aperture obtained for the samples is in the WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001 range of 72 to 226 microns and hence the average aperture can be assumed to be equal to 148. For the sake of generality, three identical samples have been tested. As such, 1-g tests are conducted for the sake of comparing the diffusion coefficient of ions obtained under normal laboratory conditions with that obtained from centrifuge tests. However, the diffusion time and the sample length are not comparable between 1-g tests of the present study and N-g tests due to scaling of diffusion time and sample length during centrifugation. Type-I Diffusion cell The diffusion cell fabricated for testing the intact rock samples, at 1-g and N-g, is depicted in Fig. 1. The cell is made of a Perspex (transparent acrylic material) cylinder of size 110mm in length with its inner and outer diameters equal to 54mm and 60mm, respectively. The cylinder is divided into three compartments by two intact rock samples of size 54.5mm in diameter and thickness, L, 3mm. The gap between the Perspex cylinder and the rock samples are sealed with silicone adhesive to avoid any leakage between the compartments. The rock samples are positioned in such a way that a large volume (approximately 200cc) is available, between the two rock samples, for filling the source solution with a certain concentration of the contaminant (C0). The two end compartments are filled with the ultrapure water with conductivity <0.5μS/cm (approximately 50cc). Each of these compartments is provided with a 6mm hole at the top with rubber seal for sampling purposes and measuring the diffused ion concentration. The two ends of the diffusion cell are sealed with the Perspex plates of size 100mm×100mm×10mm. The advantage of this type of partitioning is that two rock samples can be tested at a time. Also, sampling to measure the change in concentration of the solution is simplified. Type-II Diffusion cell The diffusion cell fabricated for testing fractured rock samples, at 1-g and N-g, is shown in Fig. 2. As shown in the figure, the diffusion cell consists of a 160mm long graduated Perspex cylinder with inner and outer diameters of 54 and 60mm, respectively. The rock sample divides this cell into a source compartment (250 cc) and a measuring compartment (~50cc). A Perspex base plate (100mm×100mm×10mm) is provided so that the cell can be placed on a horizontal surface. A fracture is created in the rock sample of thickness, L, 60mm, with the help of a rock core splitter, along its axis. The average width of the fracture, as measured by a microscope, is 0.148mm. Later, this rock sample is tight fitted in the diffusion cell and sealed (using silicone adhesive). Calibration of the Centrifuge Calibration of the centrifuge is carried out with respect to the diffusion cells designed for the study. To obtain the effective radius of rotation, r, Eq. 1 is modified as: r = (r0-tb-tm) (Eq. 6) where r0 is the maximum outer arm radius, tb is the thickness of base plate (= 10 mm) and tm is the height from the top of the base plate to the middle of the rock sample. WM’04 Conference, February 29-March 4, 2004, Tucson, AZ WM-4001