Mechanisms and Models for Bentonite Erosion Used for Geologic Disposal of High Level Radioactive Waste: A Review

The performance of the bentonite buffer in nuclear waste repository concept relies to a great extent on the buffer surrounding the canister having sufficient dry density. Loss of buffer material caused by erosion remains as the most significant process reducing the density of the buffer. In the worst case, the process is assumed to last as long as the free volume between the pellets in the pellets filled regions is filled with groundwater. Erosion rate and mass erosion are calculated based on the erosion model, and the measures are presented to prevent the geological disaster due to bentonite erosion. The groundwaters may solubilise the smectite particles in the bentonite and carry them away as colloidal particles. A dynamic model is developed for sodium gel expansion in fractures where the gel soaks up groundwater as it expands. The model is based on a force balance between and on smectite particles, which move in the water. Attractive van der Waals forces, repulsive electric diffuse layer (DDL) forces, gravity and buoyancy forces and forces caused by the gradient of chemical potential of the particles act to move the particle in the water. The effect of the fracture width and the frictions between particles and water and surrouding rock is analysed based on erosion model. The DDL forces strongly depend on the type of clay minerals and the type of ion and concentration in the water surrounding the particles. In the designed safe use of nuclear waste disposal (tens of thousands of years to hundreds of thousands of years), the safety of nuclear waste disposal is affected by the hydrodynamic and chemical effects, and bentonite erosion. Due to the bentonite erosion, the buffer/backfill layers become loose, and their permeability increases, which causes the nuclear element diffusion and convection, and even the nuclear disaster. In this paper, the mechanisms, models, experiments and control measures of bentonite erosion were systematically summarized. The current deficiencies of bentonite erosion were pointed out, and new methods were put forward to carry out the research for bentonite erosion. The measures were presented to prevent the geological disaster due to bentonite erosion through changes. The project is not only academic innovation, but also has a large practical significance. The research results of this project can be widely applied to the design, construction and maintenance of the bentonite buffer in nuclear waste repository.     

A coupled non-isothermal reactive transport model for long-term geochemical evolution of a HLW repository in clay

A numerical model of coupled saturated/unsaturated water flow, heat transfer and multi-component reactive solute transport is presented to evaluate the long-term geochemical evolution in bentonite, concrete and clay formation for a potential geological radioactive waste repository. Changes in formation porosity caused by mineral dissolution/precipitation reactions are taken into account. Simulations were carried out with a general-purpose multicomponent reactive transport code, CORE^2D V4. Numerical results show that pH in the bentonite porewater can vary from neutral to up to 13 over a time scale of 1 Ma although dissolution of silica minerals and precipitation of secondary calcium silicate hydrate (CSH) minerals in bentonite buffer the effect of the hyperalkaline plume. Mineral precipitation reduces the volume of pore space in bentonite close to the bentonite–concrete interface due to the precipitation of CSH minerals. Model results indicate that bentonite porosity decreases less than 25%. The hyperalkaline plume from the concrete only extends to a distance of 0.7 m in the clay formation over the time range of 1 Ma.     

A technique to test finite difference schemes to model some geophysical processes in a geological structure

A preliminary problem to solve in the set-up of a mathematical model simulating a geophysical process is the choice of a suitable discrete scheme to approximate the governing differential equations. This paper presents a simple technique to test finite difference schemes used in the modeling of geophysical processes occurring in a geological structure. This technique consists in generating analytical solutions similar to the ones characterizing a geophysical process, given general information on some relevant parameters. Useful information for the choice of the discrete scheme to employ in the mathematical model simulating the original geophysical process can be obtained from the comparison between the analytical solution and the approximated numerical solutions generated by means of different discrete schemes. Two classes of numerical examples approximating the differential equation that governs the steady state earth's heat flow have been treated using three different finite differences schemes. The first class of examples deals with media whose phenomenological parameters vary as continuous space functions; the second class, instead, deals with media whose phenomenological parameters vary as discontinuous space functions. The finite difference schemes that have been utilized are: Centered Finite Difference Scheme (CDS), Arithmetic Mean Scheme (AMS), and Harmonic Mean Scheme (HMS).The numerical simulations showed that: the CDS may yield physically inconsistent solutions if the lattice internodal distance is too large, but in case of phenomenological parameters varying as a continuous function, this pitfall can be avoided increasing the lattice node refinement. In case of phenomenological parameters varying as a discontinuous function, instead, the CDS may yield physically inconsistent solutions for any lattice-node refinement. The HMS produced good results for both classes of examples showing to be a scheme suitable to model situations like these.     

A new sampling technique for fluid phases in hydrothermal experiments applied to the determination of the HF-fugacities of the WFQ-buffer

A new sampling device is described which allows the separation of a fluid phase from the solid reactants in hydrothermal experiments at run conditions. The new method has been tested at temperatures up to 1,100° C at a total vapor pressure of 1 kbar.HF-concentrations of the fluid phase in equilibrium with quartz, fluorite, and wollastonite in the reaction CaF₂+SiO₂+H₂O CaSiO₃+2 HF known as the WFQ-buffer (Munoz and Eugster 1969) have been determined by direct chemical analysis using a fluoride electrode. HF-concentrations measured in the fluid phase range from 39±3 ppm at 510° C to 1,968±98 ppm at 820° C. This is equivalent to fugacities of 0.036 bar at 510° C compared to 0.033 as calculated from thermodynamic data, and 2.238 bar at 820° C compared to 2.142 bar. Equilibrium was reversed by starting out from aqueous HF-solutions in which the HF-concentrations were above or below the equilibrium value.     

Significance of conditioning to piezometric head data for predictions of mass transport in groundwater modeling

Transmissivity and head data are sampled from an exhaustive synthetic reference field and used to predict the arrival positions and arrival times of a number of particles transported across the field, together with an uncertainty estimate. Different combinations of number of transmissivity data and number of head data used are considered in each one of a series of 64 Monte-Carlo analyses. In each analysis, 250 realizations of transmissivity fields conditioned to both transmissivity and head data are generated using a novel geostatistically based inverse method. Pooling the solutions of the flow and transport equations in all 250 realizations allows building conditional frequency distributions for particle arrival positions and arrival times. By comparing these fresquency distributions, we can assess the incremental gain that additional head data provide. The main conclusion is that the first few head data dramatically improve the quality of transport predictions.     

A new laboratory set-up for measurements of electrical, hydraulic, and osmotic fluxes in clays

If clays are subjected to flows of fluid, electrical charge, chemicals, or heat, in most cases, flows of different types occur simultaneously, even if only one driving force is acting. These are so-called coupled flows. Examples of coupling phenomena are streaming potential and electroosmosis, induced by the flows of fluid and electrical charge, respectively.

Since the 1960s, laboratory devices have been constructed to measure streaming potentials and/or electroosmosis in clays or clayey soils. Due to their mechanical and hydraulic properties, clays are not easy to work with. Consequently, laboratory devices have to deal with various complications. A new design for an experimental set-up is proposed. Contrary to earlier devices, the clay sample is mounted in a flexible wall permeameter, which avoids sidewall leakage caused by the possible swell or shrink of the clay. Gold-coated gauze electrodes completely cover the surfaces of the sample, which are in contact with the solution reservoirs that ensure one-dimensional flow. In addition, the thickness of the sample is monitored during the experiment. The chemical composition of the reservoir fluids is controlled during the experiment. The device is flexible with respect to changing the solutions of both reservoirs independently, applying different hydraulic gradients, and measuring or applying electrical potentials. Finally, it is possible to mount undisturbed clay samples in the set-up, keeping them in situ during the whole experiment.

With this set-up, an extensive program of measurements of coupling phenomena like streaming potentials, electroosmosis, and membrane potentials in a sodium montmorillonite is started. Preliminary results of streaming potential measurements are presented and demonstrate that the build-up of a streaming potential due to a hydraulic gradient is a reproducible process that influences the water flow through the clay, and that the extent of the streaming potential depends on the salt concentration of the permeating solution.     

江西广丰李家膨润土压实性能研究--高放废物处置缓冲/回填材料压实性能初探

研究了广丰李家钠基膨润土的压实性能,得出了不同压实功作用下,膨润土干密度与含水率之间的关系．以及粒径、压实功等因素对压实性能的影响;在相同压实功和相同含水率条件下,膨润土粒径较小时相对应的干密度较小．当压实功为2684．9kJ／m^3时,钠基膨润土的最大干密度可达1．525g／cm^3,最优含水率为26．30％。首次选用石英砂作为添加荆,探索了添加荆对膨润土压实性能的改善作用,实验结果说明石英砂添加荆的加入可以大大提高膨润土的干密度。减小对应的最优含水率,并得出约10％的石英砂是添加剂的最佳用量。该研究结果为钠基膨润土作为高放废物处置库缓冲／回填材料的性能评价提供了重要的依据。     

A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

A space-time discontinuous Galerkin method applied to single-phase flow in porous media

A space-time discontinuous Galerkin finite element method is proposed and applied to a convection-dominant single-phase flow problem in porous media. The numerical scheme is based on a coupled space-time finite element discretization allowing for discontinuous approximations in space and in time. The continuities on the element interfaces are weakly enforced by the flux treatments, so that no extra penalty factor has to be determined. The resulting space-time formulation possesses the advantage of capturing the steep concentration front with sharp gradients efficiently. The stability and reliability of the proposed approach is demonstrated by numerical experiments. The author is grateful to the DFG (German Science Foundation—Deutsche Forschungsgemeinschaft) for the financial support under the grant number Di 430/4-2.     

A Methodology for Simulating Radionuclide Diffusion in Unsaturated Soils

In this paper, a methodology that can be employed to simulate radionuclide migration through unsaturated soils, under laboratory conditions, has been developed and reported. This was achieved with the help of a specially designed half-cell setup to study diffusion characteristics of inactive forms of Cs⁺, Sr⁺² and Co⁺² in two different types of soils, corresponding to their different compaction states. It has been noted that the apparent diffusion coefficient strongly depends on the volumetric water content of the soil. However, increase of the apparent diffusion coefficient for higher volumetric water contents is found to be much less as compared to the lower volumetric water contents.     

秦沈客运专线A14试验段软土路基加固技术研究

介绍了秦沈客运专线A14试验段软土路基工程设计施工情况。通过对各种地基处理路段沉降观测,探讨了软土路基沉降特征,推测出其最终沉降量和沉降速率,并分析了软基处理措施与沉降的关系。结果表明：软土路基沉降受加荷影响很大;采用碎石和粉喷桩处理后地基沉降量比其它处理方法要小;在松软土地层,控制填土不是主要问题。     

The use of a mixed scheme: mixed hybrid finite elements method/finite volumes (MHFE/FV), for the modeling of contaminants transport in unsaturated porous mediums

This work is intended for the development of a numerical method to simulate flows and solute transport in multiphasical porous medium taking into consideration the interaction of solid/solute. More precisely, the studied problem is modeled by a coupled system composed of an elliptical equation (for the flow) and an equation convection–diffusion–reaction (for the transfer). Numerical simulations were realistic for two-dimensional problems confirming the stability and efficiency of the combined scheme in the characterization of a pollutant transport through an unsaturated zone of an industrial site.     

Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository

We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water-saturated repository.     

A dual-porosity model for ionic solute transport in expansive clays

A microstructure model of dual-porosity type is proposed to describe contaminant transport in fully-saturated swelling clays. The swelling medium is characterized by three separate-length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the nanoscale, the medium is composed of charged clay particles saturated by a binary monovalent aqueous electrolyte solution. At the intermediate (micro) scale, the two-phase homogenized system is represented by swollen clay clusters (or aggregates) with the nanoscale electrohydrodynamics, local charge distribution, and disjoining pressure effects incorporated in the averaged constitutive laws of the electro-chemo-mechanical coefficients and the swelling pressure, which appear in Onsager’s reciprocity relations and in a modified form of Terzaghi’s effective principle, respectively. The microscopic coupling between aggregates and a bulk solution lying in the micropores is ruled by a slip boundary condition on the tangential velocity of the fluid, which captures the effects of the thin electrical double layers surrounding each clay cluster. At the macroscale, the system of clay clusters is homogenized with the bulk fluid. The resultant macroscopic picture is governed by a dual-porosity model wherein macroscopic flow and ion transport take place in the bulk solution and the clay clusters act as sources/sinks of mass of water and solutes to the bulk fluid. The homogenization procedure yields a three-scale model of the swelling medium by providing new nano and micro closure problems, which are solved numerically to construct constitutive laws for the effective electro-chemo-hydro-mechanical coefficients. Considering local instantaneous equilibrium between the clay aggregates and micropores, a quasisteady version of the dual-porosity model is proposed. When combined with the three-scale portrait of the swelling medium, the quasisteady model allows us to build-up numerically the constitutive law of the equilibrium adsorption isotherm, which governs the instantaneous immobilization of the solutes in the clay clusters. Moreover, the constitutive behavior of the retardation coefficient is also constructed by exploring its representation in terms of the local profile of the electrical double layer potential of the electrolyte solution, which satisfies the Poisson–Boltzmann problem at the nanoscale.     

A stochastic approach to optimum decomposition of cyclic patterns in sedimentary processes

This paper examines the issues of sedimentary cycles by means of reversible Markov chains. Two types of cyclic patterns in sedimentary processes are considered in terms of symmetric cycles (ABCDCBA) and asymmetric cycles (ABCDABCD). By introducing concepts of reversibility and unidirectionality, a general solution is given for decomposing all possible cyclic patterns of these two types existing in a sedimentary sequence. On the basis of two new measures f_R and f_U, the most probable trends in a sequence can be identified in an optimum way. Effective and reliable use of the technique proposed here is demonstrated by a case study.     

Application of multifractal modeling technique in systematic geochemical stream sediment survey to identify copper anomalies: A case study from Ahar,Azarbaijan, Northwest Iran

This research is based on the application of stream sediments to mineral exploration. Identifying the geochemical anomalies from background is a fundamental task in exploration geochemistry. This paper applied the element concentration–area (C–A) model, to separating the geochemical anomalies from background based on a fractal approach and for the compilation of geochemical mapping from stream sediment samples (n = 620) of the Ahar region (Iran), where some Cu mineralization occurs. Comparisons of the known copper occurrences against the anomalous area created using thresholds from C–A method illustrate these hits. All of known Cu mineralizations and moreover defines two extra Cu anomaly districts. Additional sampling (n = 186) around new Cu anomaly confirms this anomaly within the district.