Rock Matrix Diffusion Research Articles

Radionuclide transport and retardation in uplifting granitic rocks: Part 2 – Modelling coupled processes in uplift scenarios

Uplifting fractured granitic rocks occur in substantial areas of countries such as Japan. Some of these areas might be considered when siting a deep geological repository for radioactive wastes. A repository site would be selected in such an area only if it is possible to make a safety case, accounting for the changing conditions during uplift. The safety case must include robust arguments that chemical processes in the rocks around the repository will contribute sufficiently to minimise radiological doses to biosphere receptors. Numerical modelling is an important aspect of making these arguments. To provide confidence in the safety arguments, numerical models need to be sufficiently realistic, but also parameterised conservatively (pessimistically). However, model development is challenging because uplift involves many complex couplings between groundwater flow, chemical reactions between water and rock, and changing rock properties. The couplings would affect radionuclide mobilisation and retardation, by influencing diffusive radionuclide fluxes between groundwater flowing in fractures and effectively immobile porewater in the rock matrix (rock matrix diffusion, RMD) and radionuclide partitioning between water and solid phases, via: (i) mineral precipitation/dissolution; (ii) mineral alteration; and (iii) sorption/desorption. It is difficult to represent all this complexity in numerical models while showing that they are parameterised conservatively. Here we present a modelling approach, illustrated by simulation cases for some exemplar radioelements, to identify realistically conservative process conceptualisations and model parameterisations.

Groundwater–rock interactions in crystalline rocks: evidence from SIMS oxygen isotope data

AbstractThe diffusive exchange of dissolved material between fluid flowing in a fracture and the enclosing wallrocks (rock matrix diffusion) has been proposed as a mechanism by which radionuclides derived from a radioactive waste repository may be removed from groundwater and incorporated into the geosphere. To test the effectiveness of diffusive exchange in igneous and metamorphic rocks, we have carried out an investigation of veins formed at low temperatures (<100°C), comparing the oxygen isotopic composition of vein calcite with that of secondary calcite in the wallrocks. Two examples of veins from the Borrowdale Volcanic Group, Cumbria, and one from the Mountsorrel Granodiorite, Leicestershire, UK, have remarkably similar vein calcite compositions, ca. +20‰(SMOW) or greater, substantially heavier than the probable compositions of the host rocks, and these vein calcite compositions are inferred to reflect the infiltrating fluid and the temperature of vein formation. Calcites from the wallrocks are similar to those in veins, with little evidence for exchange with the wallrocks. The results support existing models for this type of vein which suggest low-temperature growth from formation brines originally linked to Permian or Triassic evaporites. The results are consistent with flow through fractures being attenuated through a damage zone adjacent to the fracture and provide no evidence of diffusional exchange with pore waters from wallrocks.

Law of Nuclide Migration in Clayey Rocks considering Diffusion and Fluid Transport

A core concern in the research on deep geological disposal of high-level radioactive waste is the migration of radionuclides in geological bodies. Most studies on radionuclide migration consider the role of only the rock fissures without incorporating the influence of the rock matrix. In this paper, the rock mass for geological disposal of high-level radioactive waste is regarded as a fissure-pore medium. Considering the influences of radionuclide diffusion and fluid transport on radionuclide migration in the process of disposal, the governing equation of radionuclide migration and evolution in the pore-fissure medium is established. The numerical scheme of the governing equation is given based on the mixed finite volume method (FVM), using our program solution module written in C++. On this basis, the numerical test model with fissures was developed, which analyzed the radionuclide migration law in clayey rocks under various fissure and rock matrix diffusion coefficients and hydraulic conductivities. The simulation results are compared with finite element method results, revealing the superiority of the mixed FVM method in solving problems of radionuclide migration in discontinuous geological bodies containing hiatuses, mutations, and fissures. The study provides a theoretical basis for evaluating the safety, feasibility, and suitability of geological disposal repositories for high-level radioactive waste in terms of radionuclide migration.

Natural analogue evidence for controls on radionuclide uptake by fractured crystalline rock

Fractured Crystalline Rocks (FCR) are being considered in several countries as hosts for radioactive waste repositories. In FCR, radionuclides may be transported relatively rapidly by bulk groundwater flow through open fractures, but much more slowly by diffusion through porewater in the rock matrices. Rock matrix diffusion (RMD) is the diffusion of radionuclides in the aqueous phase, between open fractures and rock matrices. Sorption or co-precipitation on the fracture surfaces and walls of the matrix pores causes further radionuclide retardation. RMD may be important in a repository's safety case and has been investigated by many published short-term (to a few years) laboratory and in-situ experiments. To improve understanding over longer timescales, we investigated evidence for RMD of several natural radioelements, and radioelement analogues, in five exemplar fractured crystalline rock (FCR) samples aged between c. 70 Ma and c. 455 Ma. The sample suite consisted of two samples of Borrowdale Volcanic Group (BVG) meta-tuff from northwest England, a sample of Carnmenellis Granite from southwest England and two samples of Toki Granite from central Japan. Uptake or loss of the studied elements is limited to an altered damage zone in each sample, coupled to mineral alteration processes. These zones are most extensive (a few tens of millimetres) in the Toki Granite samples. We also found unstable primary igneous minerals to persist in the immediate wallrocks of fractures in studied granite samples, suggesting that pores were not permanently water saturated in these samples. Although only a small sample suite was studied, the results show that while RMD may be important in some kinds of FCR, in others it may be negligible. Site-specific information is therefore needed to determine how much reliance can be placed on RMD when developing a safety case.

Mineral reaction kinetics constrain the length scale of rock matrix diffusion

Mass transport by aqueous fluids is a dynamic process in shallow crustal systems, redistributing nutrients as well as contaminants. Rock matrix diffusion into fractures (void space) within crystalline rock has been postulated to play an important role in the transient storage of solutes. The reacted volume of host rock involved, however, will be controlled by fluid-rock reactions. Here we present the results of a study which focusses on defining the length scale over which rock matrix diffusion operates within crystalline rock over timescales that are relevant to safety assessment of radioactive and other long-lived wastes. Through detailed chemical and structural analysis of natural specimens sampled at depth from an active system (Toki Granite, Japan), we show that, contrary to commonly proposed models, the length scale of rock matrix diffusion may be extremely small, on the order of centimetres, even over timescales of millions of years. This implies that in many cases the importance of rock matrix diffusion will be minimal. Additional analyses of a contrasting crystalline rock system (Carnmenellis Granite, UK) corroborate these results.

Numerical Modeling on Benzene Dissolution into Groundwater and Transport of Dissolved Benzene in a Saturated Fracture-Matrix System

Dissolution from residual source zones of benzene poses serious threat to the groundwater quality. Proper understanding of fate and migration of dissolved benzene is a prerequisite for planning remediation strategies to reduce groundwater contamination. In the present study, an attempt has been made to numerically model the dissolution of benzene and to investigate the transport of aqueous phase benzene in a saturated fracture-matrix system under steady-state flow condition. In addition to dissolution mass transfer, advection, dispersion and matrix diffusion of aqueous benzene has been considered along the fracture. In the present numerical model, residual phase benzene is considered to be present along the entire length of the fracture and residual phase benzene is assumed to be immobile for the flow conditions considered in the analysis. Transport equations for fracture and rock-matrix are solved using implicit finite difference method. Transport equation for aqueous benzene within the fracture has been solved in a one-dimensional domain and transport equation for aqueous benzene within rock-matrix has been solved in a pseudo-two-dimensional domain. Sensitivity studies have been conducted to investigate the impact of variation of flow velocity, dispersivity, fracture aperture, inlet benzene concentration, rock-matrix diffusion coefficient, and half fracture spacing on transport of aqueous benzene concentration within the fracture. From the present study, it can be concluded that the addition of slow liquid benzene dissolution into aqueous phase influences the benzene breakthrough curves/profiles at different velocity, fracture aperture, initial benzene concentration, mass transfer rate, rock dispersivity and half fracture spacing.

KURT 환경 자료를 이용한 가상의 다중 발생원에서의 누출 핵종의 이동 시간 평가

KURT(KAERI Underground Research Tunnel) 부지 부근에 가상의 처분장을 설정하고, 해당 부지의 세 지점에서 방사성폐기물로부터 누출된다고 가정한 방사성 핵종의 이동 시간을 계산하였다. 핵종의 이동 경로는 핵종 누출 지점에서 천부 지하수대까지로 설정하고 KURT 주변 지하수 유동계 모의를 통해 결정하였다. 세 지점은 지하수가 빠르게 유동하는 구조(highly water-conductive feature)를 지나가기 때문에 천부 지하수까지 도달하는데 상대적으로 적은 시간이 걸리는 지점으로 선정되었다. 핵종의 이동 시간은 TDRW(Time-Domain Random Walk) 기법을 통해 계산하였다. 지하수 내의 핵종의 이동 시간을 계산하기 위해, 이류(advection)와 분산(dispersion) 이외에 암반 기질(rock matrix)로의 확산(diffusion)과 기질 내부에서의 흡착(sorption)이 고려되었고, 핵종의 붕괴 및 변환에 의한 영향도 몇 개의 붕괴 사슬(decay chain)을 이용하여 계산에 반영하였다. 계산 결과를 보면, 지표 부근의 천부 지하수에 도달하는 핵종의 시간당 이동량(mass flux)은 복수의 이동 경로뿐만 아니라 핵종의 반감기와 암반 기질 내에서의 핵종의 흡착 분배 계수에 크게 영향을 받는 것으로 나타났다. 따라서 보다 안정적이고 불확실성이 감소된 심지층 처분장의 안전성 평가를 위해 우선적으로 필요한 사항으로는, 장반감기 핵종에 대한 평가가 이동 과정 이외에 저장 용기에 들어있는 상태에서부터 면밀하게 이루어져야 하고, 암반 기질에서 발생하는 핵종의 흡착 과정이 심부 현장 조건을 반영하여 평가되어야 할 것으로 생각된다. A hypothetical repository was assumed to be located at the KURT (KAERI Underground Research Tunnel) site, and the travel times of radionuclides released from three source positions were calculated. The groundwater flow around the KURT site was simulated and the groundwater pathways from the hypothetical source positions to the shallow groundwater were identified. Of the pathways, three pathways were selected because they had highly water-conductive features. The transport travel times of the radionuclides were calculated by a TDRW (Time-Domain Random Walk) method. Diffusion and sorption mechanisms in a host rock matrix as well as advection-dispersion mechanisms under the KURT field condition were considered. To reflect the radioactive decay, four decay chains with the radionuclides included in the high-level radioactive wastes were selected. From the simulation results, the half-life and distribution coefficient in the rock matrix, as well as multiple pathways, had an influence on the mass flux of the radionuclides. For enhancing the reliability of safety assessment, this reveals that identifying the history of the radionuclides contained in the high-level wastes and investigating the sorption processes between the radionuclides and the rock matrix in the field condition are preferentially necessary.

Evidence for Enhanced Matrix Diffusion in Geological Environment

Molecular diffusion in rock matrix, called as matrix diffusion, has been appreciated as a static process for elemental migration in geological environment that has been acknowledged in the context of geological disposal of radioactive waste. However, incomprehensible enhancement of matrix diffusion has been reported at a number of field test sites. Here, the matrix diffusion of saline water at Horonobe, Hokkaido, Japan is highlighted directly probing angstrom-scale pores on a field scale up to 1 km by positron–positronium annihilation spectroscopy. The first application of positron–positronium annihilation spectroscopy to field-scale geophysical research reveals the slight variation of angstrom-scale pores influenced by saline water diffusion with complete accuracy. We found widely interconnected 3 Å pores, which offer the pathway of saline water diffusion with the highly enhanced effective matrix diffusion coefficient of \(4\times 10^{-6}\) cm2 s-1. The present findings provide unambiguous evidence that the angstrom-scale pores enhance effective matrix diffusion on a field scale in geological environment.

REVIEW AND COMPILATION OF DATA ON RADIONUCLIDE MIGRATION AND RETARDATION FOR THE PERFORMANCE ASSESSMENT OF A HLW REPOSITORY IN KOREA

In this study, data on radionuclide migration and retardation processes in the engineered and natural barriers of High-Level Radioactive Waste (HLW) repository have been reviewed and compiled for use in the performance assessment of a HLW disposal system in Korea. The status of the database on radionuclide migration and retardation that is being developed in Korea is investigated and summarized in this study. The solubilities of major actinides such as D, Th, Am, Np, and Pu both in Korean bentonite porewater and in deep Korean groundwater are calculated by using the geochemical code PHREEQC (Ver. 2.0) based on the KAERI-TDB(Korea Atomic Energy Research Institute-Thermochemical Database), which is under development. Databases for the diffusion coefficients (<TEX>$D^b_e$</TEX> values) and distribution coefficients (<TEX>$K^b_d$</TEX> values) of some radionuclides in the compacted Korean Ca-bentonite are developed based upon domestic experimental results. Databases for the rock matrix diffusion coefficients (<TEX>$D^r_e$</TEX> values) and distribution coefficients (<TEX>$K^r_d$</TEX> values) of some radionuclides for Korean granite rock and deep groundwater are also developed based upon domestic experimental results. Finally, data related to colloids such as the characteristics of natural groundwater colloids and the pseudo-colloid formation constants (<TEX>$K_{pc}$</TEX> values) are provided for the consideration of colloid effects in the performance assessment.

Calibration of regional palaeohydrogeology and sensitivity analysis using hydrochemistry data in site investigations

A transient coupled regional model of groundwater flow and solute transport has been developed, which allows the use of hydrochemical data to calibrate the model input parameters. The methodology has been illustrated using examples from the Simpevarp area in south-eastern Sweden which is being considered for geological disposal of spent nuclear fuel. The 3-dimensional model includes descriptions of spatial heterogeneity, density driven flow, rock matrix diffusion and transport and mixing of different water types, and has been simulated between 8000 BC and 2000 AD. Present-day analyses of major elemental ions and stable isotopes have been used to calibrate the model, which has then been cross checked against measured hydraulic conductivities, and against the hydrochemical interpretation of reference water mixing fractions. The key hydrogeological model sensitivities have been identified using the calibrated model and are found to include high sensitivity to the top surface flow boundary condition, the influence of variations in fracture transmissivity in different orientations (anisotropy), spatial heterogeneity in the deterministic regional deformation zones and the spacing between water bearing fractures (in terms of its effect on matrix diffusion).

Numerical Modeling and Analysis of Solute Velocity and Macrodispersion for Linearly and Nonlinearly Sorbing Solutes in a Single Fracture with Matrix Diffusion

The behavior of the solute velocity and effective macrodispersivity of solute front in the fracture for the transport in a single fracture in the presence of rock matrix diffusion is analyzed using numerical modeling. The study is limited to a constant continuous solute source boundary condition in a single fracture with constant aperture. Analysis is made for linear and nonlinear sorption cases. Expressions are provided for solute velocity and effective macrodispersivity of the solute fronts during asymptotic and preasymptotic stages using spatial moment analyses. The effective retardation factor and dispersivity of solutes in the fracture are found to follow an exponential function with an exponent related to fracture-matrix parameters.

Iodine-129 constraints on residence times of deep marine brines in the Canadian Shield

Canadian Shield brines are characterized by high concentrations of both stable iodine and 1 2 9 I, the former reflecting its concentrated but diagenetically modified seawater origin, and the latter its long subsurface residence time within its host shield rocks. Stable iodine concentrations in the Yellowknife brine are as high as 18 mg/L, requiring the contribution of iodine from an external marine reservoir. This reservoir likely comprised organic-rich marine sediments in the basin where the brine was produced. Diagenesis of these sediments released iodine to the brine during its infiltration into the subsurface. 1 2 9 I concentrations in the Yellowknife brine are as high as 3.4 x 10 8 atom/L and are due to the fission of 2 3 8 U in the rock matrix and subsequent diffusion of the radiogenic 1 2 9 I into the fracture fluids. This concentration is close to the predicted secular equilibrium concentration for a fluid in basaltic rock with a uranium concentration of 1 mg/kg after the residence time of ∼80 m.y. required for secular equilibrium has been attained. This time period is interpreted as the minimum residence time of the Yellowknife brine in the shield, but it may be much greater, possibly dating back to Middle Devonian time when most of the present-day shield was covered by seawater. Similarly high stable iodine and 1 2 9 I concentrations measured in the Sudbury brine support a generic, ancient marine hypothesis for the origin of shield brines. Stable iodine and 1 2 9 I concentrations in the shallower mine waters are the result of mixing between the brine and low-iodine modern meteoric recharge that is enriched in 1 2 9 I due to global fallout from nuclear fuel waste reprocessing activities.

Analytic solutions of radionuclide transport with the limited diffusion from the fracture into a porous rock matrix

To identify the effect of the limiting zone for the matrix diffusion from an open fracture into surrounding medium recently found from field studies, full analytic solutions are derived. The solutions are then verified with existing solutions and a numerical inversion of the Laplace transform approach. The relevant field data are collected and then numerical evaluations are pursued for these complicated analytic solutions with multiple integrals. Numerical results illustrate that for given data sets the effect of limiting zone for the rock matrix diffusion can be negligible so that the current infinite rock model may underestimate the radionuclide transport through fractured porous rock.

Rock matrix diffusivity determinations by in-situ electrical conductivity measurements

A fast method to determine rock matrix diffusion properties directly in the bedrock would be valuable in the investigation of a possible site for disposal of nuclear waste. An “effective diffusivity borehole log” would provide important information on the variability of this entity over the area studied. As opposed to traditional matrix diffusion laboratory experiments, electrical conductivity measurements are fast, inexpensive and also easy to carry out in-situ. In this study, electrical resistivity data from borehole logging, as well as from measurements on the actual core, is evaluated with the purpose of extracting matrix diffusivity data. The influence of migration of ions in the electrical double layer, which can be of great importance in low ionic strength pore water, is also considered in evaluating the in-situ data to accurately determine the effective pore diffusivity. The in-situ data compare fairly well to those measured in the rock core.

A Study of Rock Matrix Diffusion Properties by Electrical Conductivity Measurements

AbstractTraditional rock matrix diffusion experiments on crystalline rock are very time consuming due to the low porosity and extensive analysis requirements. Electrical conductivity measurements are, on the other hand, very fast and larger samples can be used than are practical in ordinary diffusion experiments. The effective diffusivity of a non-charged molecule is readily evaluated from the measurements, and influences from surface conductivity on diffusion of cations can be studied. A large number of samples of varying thickness can be measured within a short period, and the changes in transport properties with position in a rock core can be examined.In this study the formation factor of a large number of Äspö diorite samples is determined by electrical conductivity measurements. The formation factor is a geometric factor defined as the ratio between the effective diffusivity of a non-charged molecule, to that of the same molecule in free liquid. The variation of this factor with position along a borecore and with sample length, and its coupling to the porosity of the sample is studied. Also the surface conductivity is studied. This was determined as the residual conductivity after leaching of the pore solution ions. The formation factor of most of the samples is in the range 1E-5 to 1E-4, with a mean value of about 5E-5. Even large samples (4-13 cm) give such values. The formation factor increases with increasing porosity and the change in both formation factor and porosity with position in the borecore can be large, even for samples close to each other.The surface conductivity increases with increasing formation factor for the various samples but the influence on the pore diffusion seems to be higher for samples of lower formation factor. This suggests that the relation between the pore surface area and the pore volume is larger for samples of low formation factor.

Specific mercury porosimetry for low-porosity materials

Modifications were made to a commercial porosimeter in order to measure very low open porosity in materials such as granites (porosity about 1%). A new measuring cell, i.e. the penetrometer, was designed with the highest possible sample holder capacity and with the capillary stem being of a smaller internal diameter than is standard. A specific computer software was also developed to take into account penetrometer distortions and granite and mercury compressions in order to correct the measured porosity values. This new apparatus was used successfully in measuring the porosity of granite from El Berrocal (Spain) as part of the European Commission Project `Rock Matrix Diffusion' (Contract No FI2W-CT91-0082). In particular, the experimental constraints were examined and the method validated by comparing the obtained results to porosities measured by water saturation.

A Stratified Channel Model with Local Longitudinal Dispersion

Modifications have been made to an existing stratified channel contaminant transport model by incorporating hydrodynamic dispersion in each channel. The integrals in the modified model are solved by a numeric method. Gaussian quadrature integration formulas were used to solve the equation, including the Gauss-Laguerre quadrature to deal with the upper infinite limit of the integral. This approach proved to be both accurate and efficient. The effects of physicochemical parameters on the elution breakthrough curve have been studied with this model. The parameters that were considered were (a) the standard deviation of a lognormal distribution of the channel width, (b) longitudinal dispersivity, (c) water velocity, (d) fracture length, (e) surface sorption coefficient, and (f) rock matrix diffusivity. Results from the calculations showed that the hydrodynamic dispersion in each channel caused additional dispersion in the elution profile. A new parameter, which quantifies rock matrix dif fusion and residence time of the solute in the fracture simultaneously, and its reference value are presented. This parameter is useful to determine numerically if the diffusion into the rock matrix is a significant contribution to the transport of the tracer through the fracture. This parameter can also be used in the design of migration experiments intended to observe diffusion into the rock matrix. The modified model has been used to analyze two independent experimental data sets obtained for a conservative tracer, one obtained in an artificial fracture and the other in a natural fracture. The results obtained with this modified model were in good agreement with both sets of experimental results. The dispersivities for both experimental systems were determined by curve fitting, and similar values were obtained for both types of fracture. The values obtained for the natural fracture especially indicated that both local hydrodynamic and channeling dispersion occurred.

Linear Response Concept Combining Advection and Limited Rock Matrix Diffusion in a Fracture Network Transport Model

This paper presents the conceptual and mathematical basis of a model for transport of nuclides in the geosphere between the near field of a radioactive waste repository and high‐conductivity fractures that are assumed to be closely connected to the biosphere. The geosphere is modeled as a network of fractures that are mapped onto a network of channels. The balance equations and boundary conditions on the scale of a single rectangular channel are given. The effects of one‐dimensional matrix diffusion in addition to advection, linear sorption in the fractures and the rock matrix, and radioactive decay are considered. A hierarchical linear response concept using Laplace transformation techniques is developed for solution of the balance equations (1) on the scale of a channel network, (2) in the individual channels, and (3) in the rock matrix adjacent to the channels. Examples with unlimited and limited matrix diffusion and for additional rock layers are discussed.

Assessment of water-filled borehole as a preferred pathway penetrating radioactive waste repository

This paper discusses the effect of human intrusion into the repository for radioactive wastes. It has been numerously suggested that an inadvertent direct drilling at the repository could provide a pathway for the release of radionuclides immobilized in waste forms even with its low occurrence probability. The diffusive mass transport in the water-filled borehole is modeled accounting for diffusion out of the waste forms and into the rock. The fully implicit integrated finite difference method is used to obtain the solution and is compared with the numerical inversion of Laplace transform method. One interesting finding is that the diffused radionuclides from the waste forms do not diffuse farther in the borehole due to low concentration gradient in early time and rock matrix diffusion so long as the borehole is not pumped continuously. The results show that the releases of radionuclides through the borehole pathway are insignificant even though the concentrations of radionuclides released into the borehole water exceed the MPC. It is shown that the model developed here could also be applied to the drilling at a non-cylindrically shaped repository and to the off-center drilling of the cylindrical repository unless the drilling occurred near the repository boundary.

Nuclide transport of decay chain in the fractured rock medium: A model using continuous time Markov process

A model using continuous time Markov process for nuclide transport of decay chain of arbitrary length in the fractured rock medium has been developed. Considering the fracture in the rock matrix as a finite number of compartments, the transition probability for nuclide from the transition intensity between and out of the compartments is represented utilizing Chapman-Kolmogorov equation, with which the expectation and the variance of nuclide distribution for the fractured rock medium could be obtained. A comparison between continuous time Markov process model and available analytical solutions for the nuclide transport of three decay chains without rock matrix diffusion has been made showing comparatively good agreement. Fittings with experimental breakthrough curves obtained with nonsorbing materials such as NaLS and uranine in the artificial fractured rock are also made.