Constraining the uncertainty in fracture geometry using tracer tests

In fractured-rock aquifers, the geometric and hydraulic properties of the fractures commonly have a dominant influence on transport. Tracer tests are often used to estimate directly the gross transport properties of a fractured rock mass. The prospects for understanding characteristics of the heterogeneities in a fractured porous medium were explored from evidence provided by tracer experiments. The approach was to simulate flow and transport on a large set of prescribed fracture networks in a two-dimensional homogeneous permeable medium, thus generating synthetic tracer test data. The fracture orientation, aperture, spacing and network geometry were systematically altered from one case to the next. A classification scheme was devised for the tracer breakthrough curves using principal component analysis and this classification was linked to the fracture pattern properties. Even under highly simplified and controlled conditions, quite different fracture patterns can produce very similar breakthrough curves. The classification scheme thus demonstrates that a single breakthrough curve cannot reveal the fracture geometry with any precision. However, the scheme provided a methodology for rejecting geometric properties that do not belong to the fracture pattern under investigation, thus reducing the uncertainty in fracture geometry.     

Modeling of Cs+ diffusion and retention in the DI-A2 experiment (Mont Terri). Uncertainties in sorption and diffusion parameters

In the DI-A2 experiment several non-reactive and reactive tracers were injected as a pulse in a packed-off borehole in the Opalinus Clay. Unlike the previous DI-A1 test, the design of the Teflon filter in the injection borehole forced the water to flow through the filter and the open space between the filter and the borehole wall (the filter itself did not act as a diffusion barrier between the circulating solution and the rock). The decrease in tracer concentration in the liquid phase was monitored during a period of a year. Afterwards, the borehole section was overcored and the tracer profiles in the rock were analyzed. A main interest of this experiment was to understand the chemical behavior of sorbing tracers: Cs⁺ (stable), ⁸⁵Sr²⁺, ⁶⁰Co²⁺ and Eu³⁺ (stable). The complete dataset (except for Eu³⁺ because of strong sorption to experimental equipment) was analyzed in a previous study with a 2D diffusion–reaction model and the derived diffusion and sorption parameters were compared with laboratory data. As in DI-A1, a difference by a factor of about 2 for sorption (magnitude of the Freundlich isotherm) was obtained between in situ and laboratory batch sorption experiments.Recent experimental and modeling studies have shown equivalent Cs⁺ sorption on intact and disaggregated Opalinus Clay samples. In view of these developments, new modeling of Cs⁺ diffusion and retention in the DI-A2 experiment has been performed using CrunchFlow. The calculations include transport by diffusion and a multisite cation exchange model to account for the retention of Cs⁺. The new results show that upscaling of Cs⁺ sorption from laboratory to field is no longer required. However, a difference in sorption by a factor of about 2 is still explained by the use of different versions of the same cation exchange model (a small difference in the selectivity coefficient for one type of site). This uncertainty in sorption leads to an uncertainty in the effective diffusion coefficient (D_e) for Cs⁺, also by a factor of 2 (2–4 × 10⁻¹⁰ m²/s). Clearly, the values of D_e obtained are correlated with the strength of sorption in the model, with stronger sorption leading to larger D_e values. Discrimination between the two versions of the exchange model is not possible when using only the results of the in situ test. Additionally, during early times (t < 10 days) the drop in Cs⁺ concentration in the circulation system is slower than expected. Due to the experimental setup, this slow decrease in concentration cannot be caused by the filter in the contact between borehole and rock. Poor mixing in the circulation system could explain this effect.     

B and Li isotopes as intrinsic tracers for injection tests in aquifer storage and recovery systems

Boron and Li isotopes have been tested as environmental tracers of treated sewage injected into a sandy aquifer (Shafdan reclamation project, Israel). During a 38 days injection test in a newly dug injection well, a conservative artificial tracer (Br⁻) was monitored together with δ¹¹B and δ⁷Li in the injectate, in the unsaturated soil zone (porous cup) and an observation well in the aquifer. In spite of B and Li concentrations in the injectate close to background values, significant shifts of the isotope signatures could be observed over the duration of the injection test. Boron isotope ratios show a breakthrough curve delayed with respect to Br⁻ breakthrough due to some reversible sorption on the aquifer material. No isotope fractionation was observed in the unsaturated or the saturated zone so that B isotopes can be considered as conservative in the investigated part of the aquifer system. Lithium isotopes are strongly fractionated, probably due to sorption processes. Lithium concentrations point to a Li sink in the system, δ⁷Li values vary strongly with a tendency of ⁷Li depletion in the liquid phase over the duration of the experiment. This is opposite to the expected preferential sorption of ⁶Li onto clay minerals. Boron isotopes reveals a valuable tracer of artificial recharge of freshwaters derived from treated sewage, both for short term tracer tests and for long-term monitoring of artificial recharge, even if in aquifers with higher clay contents, sorption-linked isotope fractionation cannot be excluded. More data are needed on Li isotope fractionation in natural groundwater systems to assess the potential of this tracer as monitoring tool.     

A method for determining both diffusion and sorption coefficients of rock medium within a few days by adopting a micro-reactor technique

Migration properties characterized by physico-chemical factors such as distribution coefficient (K_d) and diffusion coefficient (D_e) are of great concern in performance assessment of high-level radioactive waste disposal in a deep geologic environment. These coefficients are normally obtained with different sample geometries using conventional methods, i.e., crushed samples by the batch sorption method for K_d determination and block samples by the through-diffusion method for D_e. A size dependence on both K_d and D_e has been reported and an additional correction due to size difference is required to maintain consistency of the data set. A fast method was developed, hereafter referred to as the micro-channel method, to determine both the sorption coefficient (R_d) and D_e using non-crushed rock sample by adopting the micro-reactor technique. In this method, a radionuclide solution is injected into a micro-channel (20 mm length, 4 mm width, 160 μm depth), which is in contact with a plate-shaped rock sample. A part of the injected radionuclide can diffuse into the rock matrix and/or adsorb on the rock surface and this results in an inlet-outlet concentration difference. A breakthrough curve is easily obtained with a short observation period because the injection amount is extremely small and is comparable to that escaping by diffusion into the matrix. The breakthrough curve is analyzed by a two-dimensional diffusion-advection equation to evaluate R_d and D_e.In the present study, tritiated water (specific activity, 1.2 × 10⁴ Bq/mL; pH, 6) was injected into the micro-channel, and the breakthrough curve of ³H obtained. A series of experiments was carried out by changing the flow rate of the tritiated water (2.6 × 10⁻⁵–7.7 × 10⁻⁴ m/s). Rock samples were biotite granite from the Makabe area, Japan. The diffusion coefficient evaluated by least squares fitting to the numerical solutions (D_e = 1.5 × 10⁻¹¹ m²/s) agreed well with that obtained by the through-diffusion method (1.3 × 10⁻¹¹ m²/s). The breakthrough curve of Cs ([Cs] = 1.0 × 10⁻⁷ mol/L, pH 6) labeled with ¹³⁴Cs (specific activity adjusted to 4.9 × 10¹ Bq/mL) was also obtained. A nearly constant R_d value (5.5 × 10⁻² m³/kg) was found when the flow rate was less than 2.5 × 10⁻⁴ m/s. This implied that the sorption equilibrium is reached and K_d is obtained by the present method. This value was almost identical to K_d obtained by the batch sorption method (5.0 × 10⁻² m³/kg), but the testing period was very different; 1 day and 7 days, respectively. It is concluded that application of the micro-channel method provided advantages when compared with the conventional methods.     

On matrix diffusion: formulations, solution methods and qualitative effects

 Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ _m ² R _m D _m  / L _m ², whereas late-time behavior (long tracer tests) depends only on φ _m R _m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. Received, October 1997 · Revised, November 1997 · Accepted, December 1997     

Effect of different transport observations on inverse modeling results: case study of a long-term groundwater tracer test monitored at high resolution

Conservative tracer experiments can provide information useful for characterizing various subsurface transport properties. This study examines the effectiveness of three different types of transport observations for sensitivity analysis and parameter estimation of a three-dimensional site-specific groundwater flow and transport model: conservative tracer breakthrough curves (BTCs), first temporal moments of BTCs (m ₁), and tracer cumulative mass discharge (M _d) through control planes combined with hydraulic head observations (h). High-resolution data obtained from a 410-day controlled field experiment at Vandenberg Air Force Base, California (USA), have been used. In this experiment, bromide was injected to create two adjacent plumes monitored at six different transects (perpendicular to groundwater flow) with a total of 162 monitoring wells. A total of 133 different observations of transient hydraulic head, 1,158 of BTC concentration, 23 of first moment, and 36 of mass discharge were used for sensitivity analysis and parameter estimation of nine flow and transport parameters. The importance of each group of transport observations in estimating these parameters was evaluated using sensitivity analysis, and five out of nine parameters were calibrated against these data. Results showed the advantages of using temporal moment of conservative tracer BTCs and mass discharge as observations for inverse modeling.     

A plug flow-through reactor for studying biogeochemical reactions in undisturbed aquatic sediments

A slow flow, plug-through reactor was developed for measuring equilibrium and kinetic parameters of biogeochemical reactions on intact sections of sediment cores. The experimental approach was designed to preserve the structural, geochemical and microbiological integrity of the sediment sections and, hence, retrieve reaction parameters that apply to in-situ conditions.Inert tracer breakthrough experiments were performed on a variety of unconsolidated surface sediments from lacustrine, estuarine and marine depositional environments. The sediments studied cover wide ranges of composition, porosity (46–83%) and mean grain size (10⁻⁴−10⁻² cm). Longitudinal dispersion coefficients were determined from the breakthrough curves of Br⁻. The curves were also used to check for early breakthrough or trailing, that is, features indicative of non-ideal flow conditions. Sediment plugs that exhibited these features were eliminated from further experiments.Dimensionless equilibrium adsorption coefficients (K) of NH₄⁺, were calculated from measured retardation times between the breakthrough of NH₄⁺ and Br⁻. The values of K at 5°C vary between 0.3 and 2.3, with the highest value obtained in a fine-grained marine sediment, the lowest in a coarse-grained lake sediment. The values for the marine and estuarine sediments agree with values reported in the literature. The dependencies of K on ionic strength (range 0.2-0.7m) and temperature (range 5–25°C) in an estuarine sediment confirm that the main sorption mechanism for NH₄⁺ is ion exchange.The reactor was used in recirculation mode to measure steady-state rates of dissimilatory SO₄²⁻ reduction in a salt-marsh sediment. Recirculation homogenizes solute concentrations within the reactor, hence facilitating the derivation of reaction rate expressions that depend on solution composition. The rate of microbial S0₄⁻ reduction was found to be nearly independent of the dissolved SO₄²⁻ concentration in the range of 2.2−1 mM. Fitting of the experimental rates to a Monod relationship resulted in a maximum estimate of the half-saturation concentration, K_s, of 240 μM. This value is comparable to those reported for a pure culture of SO₄²⁻-reducing bacteria, but is significantly smaller than the only other K_s value reported in the literature for SO₄²⁻ utilization in a natural marine sediment.     

Characterization of flow and transport dynamics in karst aquifers by analyzing tracer test results in conduits and recharge areas (the Egino Massif,Basque Country,Spain): environmental and management implications

Karst aquifers contribute to supplying drinking water to almost a quarter of the world´s population. Their complex dynamics requires specific approaches aimed at recognizing their singularities, analyzing its vulnerability, and ensuring water resources quality. In this paper, the results of processing and modeling five breakthrough tracer curves obtained under different hydrodynamic conditions in the main conduit of Egino karst aquifer (Basque Country, Spain) are analyzed together with those involving pressure injections of the tracer in the saturated zone of the karst massif recharge area. In the conduit, transport is immediate and highly efficient (recovery rates above 84% and dispersion coefficients from 15.04 to 84.35 m²/min); tracer retentions increase as flow rates decrease and no significant contributions to its surroundings are observed. In contrast, tracer transport from the massif recharge area is more complex: after injection at a pressure of 1 MPa, most tracer remains in the surrounding of the injection borehole, retained in a saturated medium of low effective fracture porosity (? _f ?=?1.02?×?10^?4, assuming a radial divergent flow model); subsequently, the main tracer mobilization to the spring was registered with the first rains, with 0.088 m/min mean velocity and high concentrations per unit mass being injected (C _p /M₀?=?0.03 mg/L/kg), which is evidence that the tracer reaches soon the karst conduit network. In any case, a decreasing tracer presence is registered at the injection zone during a hydrological cycle. In both cases, the observed non-linearity of transport processes should be considered in the development of vulnerability approaches, modeling efforts, and mapping. Furthermore, in the case of karst massif recharge areas, as the presence of pollutants may have a significant impact on the springs and persist over time, their management and protection needs must be revised in each specific site. Simultaneously, quality-monitoring programs at the springs must be adapted to the aquifers recognized dynamics.     

Kinetics of Cd sorption, desorption and fixation by calcite: A long-term radiotracer study

Time-dependent sorption and desorption of Cd on calcite was studied over 210 days utilizing ¹⁰⁹Cd as a tracer to distinguish between ‘labile’ and ‘non-labile’ forms of sorbed Cd. Stabilizing the calcite suspensions for 12 months under atmospheric P_CO2 and controlled temperature was necessary to reliably follow Cd dynamics following initial sorption. Results revealed time-dependant Cd sorption and marked desorption hysteresis by calcite under environmentally relevant conditions. Data obtained were fitted to a first-order kinetic model and a concentric shell diffusion model. Both models described the progressive transfer of Cd²⁺ to a less reactive form within calcite and subsequent desorption of Cd subject to different initial contact times. The kinetic model provided a better fit to the combined sorption and desorption data (R² = 0.992). It differentiates between two ‘pools’ of sorbed Cd²⁺ on calcite, ‘labile’ and ‘non-labile’, in which labile sorbed Cd is in immediate equilibrium with the free Cd²⁺ ion activity in solution whereas non-labile Cd is kinetically restricted. For the diffusion model (R² = 0.959), the rate constants describing Cd dynamics in calcite produced a half-life for Cd desorption of ∼175 d, for release to a ‘zero-sink’ solution. Results from this study allow comment on the likely mechanisms occurring at the calcite surface following long-term Cd sorption.     

Diffusion and sorption of Cs, I and HTO in samples of the argillaceous Wakkanai Formation from the Horonobe URL, Japan: Clay-based modeling approach

Diffusion and sorption behaviors of cationic Cs⁺, anionic I⁻ and neutral HTO in samples of the Wakkanai Formation from the Horonobe underground research laboratory (URL), Japan, were investigated as a function of ionic strength (I) of synthetic groundwater by through-diffusion and batch sorption experiments and mechanistic modeling. The effective diffusivities (D_e) measured by through-diffusion experiments showed cation excess and anion exclusion effects, which were strongly dependent on I; D_e for Cs⁺ decreased as I increased, D_e for I⁻ showed the opposite dependency and D_e for HTO showed no dependence. The sorption of Cs⁺ measured by through-diffusion and batch sorption experiments were described by Freundlich isotherms with consistent parameters and decreased with I as a result of competitive ion exchange.Diffusion and sorption behaviors were interpreted by assuming the clay components of illite and smectite control diffusion and sorption mechanisms. The component additive (CA) sorption model, which includes illite and smectite contents and their ion exchange constants, provided a reasonable account of the Cs⁺ sorption trends measured as functions of I and Cs concentration. The diffusion model was developed by coupling the electrical double layer (EDL) model, describing the change of ionic concentrations (cation excess and anion deficit) and viscoelectric effects caused by electrostatic interaction at negatively charged clay surfaces, and a simplified pore model assuming one type of pore shape and includes their size distribution. When averaging the electrostatic effects by using the pore surface area distribution, the model could predict the cation excess and anion exclusion effects, and its dependence on I reasonably well. This result implies the nanoscale pores dominating the pore surface area can strongly impact on ionic diffusion in argillaceous rocks. The clay-based modeling approach described here provides a useful tool to predict ionic diffusion and sorption in argillaceous rocks.     

Estimating regional-scale fractured bedrock hydraulic conductivity using discrete fracture network (DFN) modeling

Estimating bedrock hydraulic conductivity of regional fractured aquifers is challenging due to a lack of aquifer testing data and the presence of small and large-scale heterogeneity. This study provides a novel approach for estimating the bedrock hydraulic conductivity of a regional-scale fractured bedrock aquifer using discrete fracture network (DFN) modeling. The methodology is tested in the mountainous Okanagan Basin, British Columbia, Canada. Discrete fractures were mapped in outcrops, and larger-scale fracture zones (corresponding to lineaments) were mapped from orthophotos and LANDSAT imagery. Outcrop fracture data were used to generate DFN models for estimating hydraulic conductivity for the fractured matrix (K _m). The mountain block hydraulic conductivity (K _mb) was estimated using larger-scale DFN models. Lineament properties were estimated by best fit parameters for a simulated pumping test influenced by a fracture zone. Unknown dip angles and directions for lineaments were estimated from the small-scale fracture sets. Simulated K _m and K _mb values range from 10^–8 to 10^–7?m/s and are greatest in a N–S direction, coinciding with the main strike direction of Okanagan Valley Fault Zone. K _mb values also decrease away from the fault, consistent with the decrease in lineament density. Simulated hydraulic conductivity values compare well with those estimated from pumping tests.     

The determination of SO42-, NaSO4-, and MgSO40 tracer diffusion coefficients and their application to diagenetic flux calculations

Sulfur-35 was used to monitor the non-steady-state tracer diffusion of the free sulfate ion and sulfate ion-pairs in aqueous solutions of MgSO₄ and Na₂SO₄. Diffusion coefficients were derived from radiotracer flux measurements taken over ionic strengths ranging from 0.001 to 0.7. The experimental tracer diffusion coefficient is a function of the diffusion coefficients of the free sulfate ion and the sulfate ion-pairs as well as the ion pair equilibrium constant. The free sulfate ion tracer diffusion coefficient was determined independently from both the MgSO₄ and Na₂SO₄, experiments and found to be 1.11 and 1.08 (in units of 10^-5cm²sec^-1, ± 10%, respectively. These values closely agree with that calculated from the Nernst expression, 1.07 sx 10^-5cm²sec^-1. The tracer diffusion coefficients of MgSO₄⁰ and NaSO₄^- were determined to be 0.85 and 1.23 sx 10^-5cm²sec^-1, respectively. These numbers are in reasonable agreement with the earlier work on mutual diffusion coefficients by Rard and Miller (1979b) (D_MgSO4^o = 0.65, D_naso4^- = 1.19) and Harned and Hudson (1951)D_MgSO4⁰ = (0.70). A modified version of the theoretical equation developed by Pikal (1971) is proposed for predicting the tracer diffusion coefficients of many ion-pairs relevant to seawater. Many of these predicted values are found to be within 10–20% of the empirical values extracted from mutual diffusion data. The experimental and theoretical diffusion coefficient data are used to calculate revised coupled diffusion coefficients, D^g, according to the model of Lasaga (1979).     

Experimental determination of the diffusion coefficient for calcium in olivine between 900°C and 1500°C

Experiments have been carried out to determine the temperature, oxygen fugacity (fO₂) and compositional dependence of the tracer diffusion coefficient (D) of calcium in olivine. These data constrain the diffusion coefficient over the temperature range 900 to 1500°C for the three principal crystallographic axes. Well constrained linear relationships between the reciprocal of the absolute temperature and log(D) exist at any given oxygen fugacity. There is a strong dependence of the diffusion coefficient on oxygen fugacity with D ∝ fO₂^(1/3). This makes a knowledge of the T-fO₂ path followed by geological samples a prerequisite for modelling Ca diffusion in olivine. The best fitting preexponential factor (Do) and activation energy (E) to the Arrhenius equation log (D) = log [Do exp(−E/RT)] + 0.31Δ log fO₂ for Ca diffusion in olivine at a given oxygen fugacity (fO₂*) are given by:diffusion along [100]: log [Do (m²/s)] = −10.78 ± 0.43; E = 193 ± 11 kJ/moldiffusion along [010]: log [Do (m²/s)] = −10.46 ± 0.37; E = 201 ± 10 kJ/moldiffusion along [001]: log [Do (m²/s)] = −10.02 ± 0.29; E = 207 ± 8 kJ/molwhere Δ log fO₂ = log[fO₂*] − log[10⁻¹²] with fO₂* in units of bars. There is no measurable compositional dependence of the diffusion coefficient between Fo₈₃ and Fo₉₂. Diffusion in Fo₁₀₀ has a much higher activation energy than in Fe-bearing olivine and has a weaker fO₂ dependence.     

Dynamics Of Karstification: A Model Applied To Hydraulic Structures In Karst Terranes

To model the development of karst channels from primary fissures in limestone, a computer simulation of solutional widening of a fracture by calcite agressive water is proposed. The parameters defining the problem are the initial width a₀ of the fracture, its length l, and the hydraulic gradient i driving water through it. The dissolution rates limestone determine how fast enlargement of the fractures proceeds. At a calcite concentration, c, far from equilibrium, the dissolution follows a first-order rate law, F⁽¹⁾=α₀(c_eq-c); close to the equilibrium concentration, c_eq, a slow fourth-order rate law F⁽⁴⁾=β₀(c_eq-c)⁴ is valid. The results show that, at the time of initiation, the water flow through the karst channels increases slowly in time until an abrupt increase occurs. After this moment of breakthrough, the channel enlarges rapidly and evenly over its entire length by first-order kinetics. Breakthrough times have been calculated for karstification under natural conditions for low hydraulic gradients as functions of a₀, l, and i. Special attention is given to karstification in the vicinity of hydraulic structures where hydraulic gradients are high (>0.5) and channel lengths are below 200 m. We find that the breakthrough event will occur in less than 100 years, if: (i/l) > (5.3·10^?8a₀ ^?2.63P_CO2 ^?0.77) where l is in m and a₀ is in cm, (i/l) is given in m^-1, and P_CO2[atm] is the CO₂ pressure of the water entering the fracture. After this event, the channels will widen to a width of about 1 cm within only 10 years, which can cause considerable leakage near or through hydraulic structures. Finally, critical values of the parameters i, l, a₀, which give the conditions of failure in various types of hydraulic structures are discussed.     

Translation of field tracer-test results into bounding predictions of matrix diffusion in the shallow subsurface at Idaho National Laboratory, USA

Matrix-diffusion parameters deduced from an infiltration tracer test at Idaho National Laboratory (INL), USA, are combined with other site information in an analysis involving two dimensionless lumped parameters to assess the effects of matrix diffusion on contaminant transport at the INL over longer distance and time scales than were evaluated in the test. Matrix diffusion was interrogated in the test by comparing, in three different observation wells, the breakthrough curves of two simultaneously injected nonsorbing solutes that have different diffusion coefficients. The matrix-diffusion parameters deduced from the different breakthrough curves were in good agreement, suggesting that the parameters may be broadly applicable at the INL. With this in mind, the uncertainties in the individual parameters that make up the two lumped parameters were estimated, and the resulting ranges of parameter values were used to assess matrix diffusion over larger scales. Assessments of the effects of flow transients, spatial heterogeneity in transport parameters, and sorption on solute transport in the shallow subsurface flow system were also conducted. The methods presented here should be generally applicable to other settings for making bounding assessments of the effects of matrix diffusion while honoring the information obtained from tracer tests and other supporting data.     

Analytical solutions of tracer transport in fractured rock associated with precipitation-dissolution reactions

Precipitation-dissolution reactions are important for a number of applications such as isotopic tracer transport in the subsurface. Analytical solutions have been developed for tracer transport in both single-fracture and multiple-fracture systems associated with these reactions under transient and steady-state transport conditions. These solutions also take into account advective transport in fractures and molecular diffusion in the rock matrix. For studying distributions of disturbed tracer concentration (the difference between actual concentration and its equilibrium value), effects of precipitation-dissolution reactions are mathematically equivalent to a “decay” process with a decay constant proportional to the corresponding bulk reaction rate. This important feature significantly simplifies the derivation procedure by taking advantage of the existence of analytical solutions for tracer transport associated with radioactive decay in fractured rock. It is also useful for interpreting tracer breakthrough curves, because the impact of a decay process is relatively easy to analyze. Several illustrative examples are presented, which show that the results are sensitive to fracture spacing, matrix diffusion coefficient (fracture surface area), and bulk reaction rate (or “decay” constant), indicating that the relevant flow and transport parameters may be estimated by analyzing tracer signals.     

The influence of Fe(II) competition on the sorption and migration of Ni(II) in MX-80 bentonite

The results from batch sorption experiments on montmorillonite systems have demonstrated that bivalent transition metals compete with one another for sorption sites. For safety analysis studies of high level radioactive waste repositories with compacted bentonite near fields, the importance of competitive sorption on the migration of radionuclides needs to be evaluated. Under reducing conditions, the bentonite porewater chosen has a Fe(II) concentration of ∼5.3 × 10⁻⁵ M through saturation with siderite. The purpose of this paper is to assess the influence of such high Fe(II) concentrations on the transport of Ni(II) through compacted bentonite, Ni(II) was chosen as an example of a bivalent transition metal. The one-dimensional calculations were carried out at different Ni(II) equilibrium concentrations at the boundary (Ni(II)_EQBM) with the reactive transport code MCOTAC incorporating the two site protolysis non electrostatic surface complexation/cation exchange sorption model, MCOTAC-sorb. At a Ni(II)_EQBM level of 10⁻⁷ M without Fe(II) competition, the reactive transport calculations using a constant K_d approach and the MCOTAC-sorb calculation yielded the same breakthrough curves. At higher Ni(II)_EQBM (10⁻⁵ M), the model calculations with MCOTAC-sorb indicated a breakthrough which was shifted to later times by a factor of ∼5 compared with the use of the constant K_d approach.When sorption competition was included in the calculations, the magnitude of the influence depended on the sorption characteristics of the two competing sorbates and their respective concentrations. At background Fe(II) concentrations of 5.3 × 10⁻⁵ M, and a Ni(II)_EQBM level of 10⁻⁷ M, the Ni(II) breakthrough time was ∼15 times earlier than in the absence of competition. At such Fe(II) concentrations the Ni(II) breakthrough curves at all source concentrations less than 3.5 × 10⁻⁵ M (fixed by the NiCO_3,S solubility limit) are the same i.e. Ni(II) exhibits linear (low) sorption.Competitive sorption effects can have significant influences on the transport of radionuclides through compacted bentonite i.e. reduce the migration rates. Since, for the case considered here, the Fe(II) concentration in the near field of a high-level radioactive waste repository may change in time and space, the transport of bivalent transition metal radionuclides can only be properly modelled using a multi-species reactive transport code which includes a sorption model.     

Method for the determination of residual carbon dioxide saturation using reactive ester tracers

The mechanisms for storage of CO₂ in rock formations include structural/stratigraphic, mineral, solubility and residual trapping. Residual trapping is very important in terms of both containment security and storage capacity. However, to date, the contribution from residual trapping (i.e. immobilisation of supercritical fluid via capillarity in pore spaces) is still relatively difficult to quantify accurately. Using a laboratory-based testing program, this study demonstrates the feasibility of using reactive ester tracers (i.e. triacetin, propylene glycol diacetate and tripropionin), which partition between a mobile water phase and a stationary supercritical CO₂ phase, to quantify the residual CO₂ saturation, S_gr, of a rock formation. The proposed single-well test involves injecting these tracers into the subsurface, followed by CO₂ saturated water, where the ester tracers slowly hydrolyse to form products with differing partition coefficients. After a suitable period of time, allowing for partial hydrolysis, water containing the tracer mixture is produced from the subsurface and analysed using gas chromatography mass spectrometry (GCMS). A numerical simulator of the tracer behaviour in a reservoir is used to explain the differential breakthrough of these tracer compounds during water production to estimate S_gr. Computer modelling suggests that the use of esters tracers to determine CO₂ residual saturation is a potentially robust method. The supercritical CO₂/water partition coefficients directly dictate the amount of time that each tracer spends in the CO₂ and water phases. As such for modelling of tracer behaviour and estimating S_gr, knowing the tracer partition coefficient is essential; in this paper, the first laboratory study to determine the partition coefficients of these reactive ester tracers is described.