A technique for estimating one-dimensional diffusion coefficients in low-permeability sedimentary rock using X-ray radiography: comparison with through-diffusion measurements

The measurement of diffusive properties of low-permeability rocks is of interest to the nuclear power industry, which is considering the option of deep geologic repositories for management of radioactive waste. We present a simple, non-destructive, constant source in-diffusion method for estimating one-dimensional pore diffusion coefficients (D(p)) in geologic materials based on X-ray radiography. Changes in X-ray absorption coefficient (Deltamicro) are used to quantify changes in relative concentration (C/C(0)) of an X-ray attenuating iodide tracer as the tracer solution diffuses through the rock pores. Estimated values of D(p) are then obtained by fitting an analytical solution to the measured concentration profiles over time. Measurements on samples before and after saturation with iodide can also be used to determine iodide-accessible porosity (phi(I)). To evaluate the radiography method, results were compared with traditional steady-state through-diffusion measurements on two rock types: shale and limestone. Values of D(p) of (4.8+/-2.5)x10(-11) m(2).s(-1) (mean+/-standard deviation) were measured for samples of Queenston Formation shale and (2.6+/-1.0)x10(-11) m(2).s(-1) for samples of Cobourg Formation limestone using the radiography method. The range of results for each rock type agree well with D(p) values of (4.6+/-2.0)x10(-11) m(2).s(-1) for shale and (3.5+/-1.8)x10(-11) m(2).s(-1) for limestone, calculated from through-diffusion experiments on adjacent rock samples. Low porosity (0.01 to 0.03) and heterogeneous distribution of porosity in the Cobourg Formation may be responsible for the slightly poorer agreement between radiography and through-diffusion results for limestones. Mean values of phi(I) for shales (0.060) and limestones (0.028) were close to mean porosity measurements made on bulk samples by the independent water loss technique (0.062 and 0.020 for shales and limestones, respectively). Radiography measurements offer the advantage of time-saving for diffusion experiments because the experiment does not require steady-state conditions and also allows for visualization of the small-scale heterogeneities in diffusive properties within rocks at the mm to cm scale.     

Effect of temperature on the containment properties of argillaceous rocks: The case study of Callovo-Oxfordian claystones

Heat generated by high level radioactive wastes could alter the performance of a clay repository. It was intended to investigate the effect of such a thermal period on the diffusive properties of Callovo-Oxfordian claystones. Thus, through-diffusion experiments with HTO, Cl-36, Na-22 and Cs-137 were performed before, during and after stages of heating at 80°C that lasted for up to one year. A special attention was paid to limit the occurrence of any chemical disturbance. Therefore (i) the temperature was raised to 80°C, then progressively brought back to 21°C, thanks to three intermediate temperature stages, and (ii) specific synthetic solutions were used for each temperature, chemistry of which being close to the equilibrium state, especially with respect to the carbonate and sulphate minerals. It was found that experiments carried out at 80°C showed a clear increase of the effective diffusion coefficient values for the four tracers with respect to those obtained at 21°C (by a factor of 3 for HTO and Cl-36, 5 for Na-22 and 2 for Cs-137). On the other hand, the porosity and rock capacity values did not exhibit any significant discrepancy between 21°C and 80°C, indicating no observable damage of both the pore conducing network and the sorption properties of clay minerals. The Stokes-Einstein relationship, based on the temperature dependency of the viscosity of bulk water, could be used to describe the temperature dependence of the diffusion of HTO and Cl-36 but failed to describe the diffusive evolution of the two sorbing cations, Na-22 and Cs-137. Furthermore, experiments performed after the thermal period led to diffusive properties well matching those obtained before heating. All these results suggest that at the lab scale the heating of rock samples would not alter the claystone containment properties.     

Contribution of the diffusive exchange method to the characterization of pore-water in consolidated argillaceous rocks

Consolidated argillaceous rocks, potential host rocks for nuclear waste disposal, display particular properties (low water content, very small pore size) that require specific methods, especially for the characterization of their pore-water. The diffusive exchange method was applied to the claystone of Tournemire by taking into account the effect of swelling or micro-cracks induced by drilling. The good agreement of diffusion parameters with those obtained from the through-diffusion method showed that the extent of this disturbance was low. This method led to stable isotope content values in pore-water in good agreement with those measured in the fracture fluids located in the vicinity, validating the method. On the contrary, the vacuum distillation technique gave a systematic depletion in heavy isotopes of water, probably induced by an incomplete extraction of pore-water. For the chloride tracer, the determination of the accessible porosity on each sample allowed the estimate of chloride concentration of pore-water to be improved, by taking into account all the petrophysical heterogeneities.     

A laboratory experiment for determining both the hydraulic and diffusive properties and the initial pore-water composition of an argillaceous rock sample: a test with the Opalinus clay (Mont Terri, Switzerland)

Argillaceous formations are thought to be suitable natural barriers to the release of radionuclides from a radioactive waste repository. However, the safety assessment of a waste repository hosted by an argillaceous rock requires knowledge of several properties of the host rock such as the hydraulic conductivity, diffusion properties and the pore water composition. This paper presents an experimental design that allows the determination of these three types of parameters on the same cylindrical rock sample. The reliability of this method was evaluated using a core sample from a well-investigated indurated argillaceous formation, the Opalinus Clay from the Mont Terri Underground Research Laboratory (URL) (Switzerland). In this test, deuterium- and oxygen-18-depleted water, bromide and caesium were injected as tracer pulses in a reservoir drilled in the centre of a cylindrical core sample. The evolution of these tracers was monitored by means of samplers included in a circulation circuit for a period of 204 days. Then, a hydraulic test (pulse-test type) was performed. Finally, the core sample was dismantled and analysed to determine tracer profiles. Diffusion parameters determined for the four tracers are consistent with those previously obtained from laboratory through-diffusion and in-situ diffusion experiments. The reconstructed initial pore-water composition (chloride and water stable-isotope concentrations) was also consistent with those previously reported. In addition, the hydraulic test led to an estimate of hydraulic conductivity in good agreement with that obtained from in-situ tests.     

Determination of sorption properties of intact rock samples: New methods based on electromigration

Two new methods for determining sorption coefficients in large rock samples have been developed. The methods use electromigration as a means to speed up the transport process, allowing for fast equilibration between rock sample and tracer solution. An electrical potential gradient acts as a driving force for transport in addition to the concentration gradient and forces the cations through the rock sample towards the cathode. The electrical potential gradient induces both electromigration and electroosmotic flow with a resulting solute transport that is large compared to diffusive fluxes. In one of the methods, the solute is driven through the sample and collected at the outlet side. In the other, simpler method, the rock sample is equilibrated by circulating the solute through the sample. The equilibration of rock samples, up to 5 cm in length, with an aqueous solution has been accomplished within days to months. Experiments using cesium as a sorbing tracer yield results consistent with considerably more time demanding in-diffusion experiments. These methods give lower distribution coefficients than those obtained using traditional batch experiments with crushed rock.     

Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity

Matrix diffusion is an important transport process in geologic materials of low hydraulic conductivity. For predicting the fate and transport of contaminants, a detailed understanding of the diffusion processes in natural porous media is essential. In this study, diffusive tracer transport (iodide) was investigated in a variety of geologically different limestone and sandstone rocks. Porosity, structural and mineralogical composition, hydraulic conductivity, and other rock properties were determined. The effective diffusion coefficients were measured using the time-lag method. The results of the diffusion experiments indicate that there is a close relationship between total porosity and the effective diffusion coefficient of a rock (analogous to Archie's Law). Consequently, the tortousity factor can be expressed as a function of total porosity. The relationship fits best for thicker samples (> 1.0 cm) with high porosities (> 20%), because of the reduced influence of heterogeneity in larger samples. In general, these correlations appear to be a simple way to determine tortuosity and the effective diffusion coefficient from easy to determine rock porosity values.     

Effect of density-driven flow on the through-diffusion experiment

Diffusion is one of the main mechanisms of solute transport in pore water of geologic media. The effective diffusion coefficient of a solute in a rock is usually measured by the through-diffusion experiment. However, in this experiment, the effect of advection, induced by density difference between dense aqueous solution and pure water, has not been considered. To evaluate the effect of density-driven flow, a through-diffusion experiment using Fontainebleau sandstone was conducted for KCl and KI aqueous solutions with various densities. The measured effective diffusion coefficients were positively correlated with the density difference; the effective diffusion coefficient of a 1 M KI solution (density difference, 0.119 g/cm³) was one order of magnitude larger than that of a 0.1 M KCl solution (density difference, 0.005 g/cm³). The result is explained by a theoretical model using a diffusion–advection equation including Darcy's law. Based on the theory, a diagram to evaluate the condition at which the measured effective diffusion coefficient does not include the effect of advection is presented.     

The effects of scale and spatial heterogeneities on diffusion in volcanic breccias and basalts: Amchitka Island, Alaska

Knowledge of the factors that influence the diffusion of contaminants, such as the diffusivity and the connected porosity, is crucial to modeling the long-term fate and transport of contaminants in subsurface systems with small or negligible advective flow, such as in fractured crystalline rock. Fractured rock is naturally heterogeneous, and hence, understanding the diffusivity of a molecule through this material (or the formation factor of the medium) becomes a complex problem, with critical concerns about the scale of laboratory measurements and about the spatial variability of these measurements relative to the scale needed for fate and transport modeling. This study employed both electrical and tracer-based laboratory methods to investigate the effects of scale and pore system connectivity on the diffusivity for volcanic matrix rock derived from the study site, a former underground nuclear test site at Amchitka Island, Alaska. The results of these investigations indicate a relatively well-connected pore system with scale effects generally limited to approximately 6 cm lengths and well-correlated to observed heterogeneous features. An important conclusion resulting from this study, however, is that there is a potential for the estimated diffusivity to be misrepresented by an order of magnitude if multiple samples or longer sample lengths are not used. Given the relatively large number of measurements resulting from these investigations, an analysis of the probability density function (PDF) of the diffusivity was possible. The PDF of the diffusivity was shown to generally follow a normal distribution for individual geologic layers. However, when all of the geologic layers are considered together, the distribution of the subsurface as a whole was shown to follow a lognormal distribution due to the order of magnitude differences amongst the layers. An understanding of these distributions is essential for future stochastic modeling efforts.     

Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron radiation

The diffusion pathways of porous sandstone were examined by a three-dimensional (3-D) imaging technique based on X-ray computed tomography (CT) using the SPring-8 (Super Photon ring-8 GeV, Hyogo, Japan) synchrotron radiation facility. The analysis was undertaken to develop better understanding of the diffusion pathways in natural rock as a key factor in clarifying the detailed mechanism of the diffusion of radionuclides and water molecules through the pore spaces of natural barriers in underground nuclear waste disposal facilities. A cylindrical sample (diameter 4 mm, length 6 mm) of sandstone (porosity 0.14) was imaged to obtain a 3-D image set of 450(3) voxels=2.62(3) mm(3). Through cluster-labeling analysis of the 3-D image set, it was revealed that 89% of the pore space forms a single large pore-cluster responsible for macroscopic diffusive transport, while only 11% of the pore space is made up of isolated pores that are not involved in long-range diffusive transport. Computer simulations of the 3-D diffusion of non-sorbing random walkers in the largest pore cluster were performed to calculate the surface-to-volume ratio of the pore, tortuosity (diffusion coefficient in free space divided by that in porous rock). The results showed that (i) the simulated surface-to-volume ratio is about 60% of the results obtained by conventional pulsed-field-gradient proton nuclear magnetic resonance (NMR) laboratory experiments and (ii) the simulated tortuosity is five to seven times larger than the results of laboratory diffusion experiments using non-sorbing I(-) and Br(-). These discrepancies are probably attributed to the intrinsic sample heterogeneity and limited spatial resolution of the CT system. The permeability was also estimated based on the NMR diffusometry theory using the results of the random walk simulations via the Kozeny-Carman equation. The estimated permeability involved an error of about 20% compared with the permeability measured by the conventional method, suggesting that the diffusometry-based NMR well logging with gradient coils is applicable to the in-situ permeability measurement of strata. The present study demonstrated that X-ray CT using synchrotron radiation is a powerful tool for obtaining 3-D pore structure images without the beam-hardening artifacts inevitable in conventional CT using X-ray tubes.     

Diffusion of tritiated water and 22Na+ through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and 22Na(+), considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test. The experimental data were inversely modelled applying an automated Marquardt-Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D(e), and the rock capacity factor, alpha. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K(d)-values were found to be consistent with R(d)-values measured in previous batch-sorption experiments. The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption. Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.     

Simultaneous estimation of effective and apparent diffusion coefficients in compacted bentonite

Effective diffusion coefficients (D(e)) are usually measured by means of "through-diffusion" experiments in which steady state is reached, and the "time-lag" methods are used to estimate the apparent diffusion coefficient (D(a)). For sorbing radionuclides (as caesium), the time needed to reach steady-state conditions is very large, and the precision in D(a) determinations is not satisfactory. In this paper, a method that allows determining simultaneously effective and apparent diffusion coefficients in compacted bentonite without reaching steady-state conditions is described. Basically, this method consists of an "in-diffusion" experiment in which the concentration profile in the bentonite sample is used to estimate D(a), and the temporal evolution of the solute concentration in the reservoir is used to estimate D(e). This method has several advantages over the typical "through-diffusion" experiments, in particular: (a) experiment duration is significantly shorter, (b) D(a) values are measured with greater precision and (c) it is not necessary to maintain a constant solute concentration in the reservoir. This new method has been used to estimate the effective and apparent diffusion coefficients for caesium in FEBEX bentonite and in order to validate it, the results have been compared with results previously obtained with standard methods. Experimental results have been satisfactorily modelled using a simple model of diffusion in porewater and the measured value of D(e)(Cs) is very similar to D(e)(HTO) in the same bentonite. There is no evidence of "surface diffusion" in FEBEX bentonite for caesium.     

Modelling radionuclide transport for time varying flow in a channel network

Water flowrates and flow directions may change over time in the subsurface for a number of reasons. In fractured rocks flow takes place in channels within fractures. Solutes are carried by the advective flow. In addition, solutes may diffuse in and out of stagnant waters in the rock matrix and other stagnant water regions. Sorbing species may sorb on fracture surfaces and on the micropore surfaces in the rock matrix. We present a method by which solute particles can be traced in flowing water undergoing changes in flowrate and direction in a complex channel network where the solutes can also interact with the rock by diffusion in the rock matrix. The novelty of this paper is handling of diffusion in the rock matrix under transient flow conditions. The diffusive processes are stochastic and it is not possible to follow a particle deterministically. The method therefore utilises the properties of a probability distribution function for a tracer moving in a fracture where matrix diffusion is active. The method is incorporated in a three dimensional channel network model. Particle tracking is used to trace out a multitude of flowpaths, each of which consists of a large number of channels within fractures. Along each channel the aperture and velocity as well as the matrix sorption properties can vary. An efficient method is presented whereby a particle can be followed along the variable property flowpath. For stationary flow conditions and a network of channels with advective flow and matrix diffusion, a simple analytical solution for the residence time distribution along each pathway can be used. Only two parameter groups need to be integrated along each path. For transient flow conditions, a time stepping procedure that incorporates a stochastic Monte-Carlo like method to follow the particles along the paths when flow conditions change is used. The method is fast and an example is used for illustrative purposes. It is exemplified by a case where land rises due to glacial rebound. It is shown that the effects of changing flowrates and directions can be considerable and that the diffusive migration in the matrix can have a dominating effect on the results.     

Formation factor logging by electrical methods. Comparison of formation factor logs obtained in situ and in the laboratory

In this paper, a new in situ method for obtaining the formation factor, which is essential for the matrix diffusion, is described and tested in intrusive igneous rock. The method is based on electrical resistivity measurements in rock where the pore water and rock resistivities are essential parameters. The method is based on electromigration instead of diffusion as in traditional diffusion experiments. In previous works, quantitative formation factors of rock have been obtained by electrical methods in the laboratory. Here, a similar approach is used in situ. An in situ logging campaign was performed by SKB during 2000 in the 1700-m-deep borehole KLX02 in Laxemar, Sweden. The rock resistivity was measured with the slimhole Dual Laterolog from Antares. The groundwater resistivity was measured with the Difference Flow Meter from Posiva. A formation factor log was obtained with the maximum vertical resolution of 10 cm. In order to validate the log, 100 rock samples were taken from the bore core, and a formation factor log was obtained by using electrical methods in the laboratory. Both direct current (DC) and alternating current (AC) were used. The measurements on the core confirmed that the in situ log was quantitative, but with a possible systematic error. The in situ formation factors were on average about 1/3 to 1/5 of the laboratory formation factors, depending on depth.     

An axisymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples

Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an axisymmetric diffusion experiment coupled with tracer profiling may be a promising approach to estimate of diffusion anisotropy of sedimentary rocks.     

Transverse vertical dispersion in groundwater and the capillary fringe

Transverse dispersion is the most relevant process in mass transfer of contaminants across the capillary fringe (both directions), dilution of contaminants, and mixing of electron acceptors and electron donors in biodegrading groundwater plumes. This paper gives an overview on literature values of transverse vertical dispersivities alpha(tv) measured at different flow velocities and compares them to results from well-controlled laboratory-tank experiments on mass transfer of trichloroethene (TCE) across the capillary fringe. The measured values of transverse vertical dispersion in the capillary fringe region were larger than in fully saturated media, which is credited to enhanced tortuosity of the flow paths due to entrapped air within the capillary fringe. In all cases, the values observed for alpha(tv) were < 1 mm. The new measurements and the literature values indicate that alpha(tv) apparently declines with increasing flow velocity. The latter is attributed to incomplete diffusive mixing at the pore scale (pore throats). A simple conceptual model, based on the mean square displacement and the pore size accounting for only partial diffusive mixing at increasing flow velocities, shows very good agreement with measured and published data.     

Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.     

Consistent interpretation of the results of through-, out-diffusion and tracer profile analysis for trace anion diffusion in compacted montmorillonite

Literature data for anion diffusion in compacted swelling clays contain systematic inconsistencies when the results of through-diffusion tests are compared with those of out-diffusion or tracer profile analysis. In the present work we investigated whether these inconsistencies can be explained by taking into account heterogeneities in the compacted samples; in particular increased porosities at the clay boundaries. Based on the combined results of out-diffusion, tracer profile analysis and the spatial distribution of the electrolyte anion in the clay, we conclude that the inconsistencies can indeed be resolved by taking into account a heterogeneous distribution of the total and the anion-accessible porosity. This, by definition, leads to a position dependence of the effective diffusion coefficient. Neglecting these effects results in a rather subordinate systematic error in the determination of effective diffusion coefficients of anions from through-diffusion tests with clay thicknesses in the centimetre range. However, stronger errors in terms of absolute values and conceptual interpretation may be introduced in out-diffusion tests and profile analyses of the diffused tracer. We recommend that anion diffusion tests should be accompanied by measurements of the total and anion-accessible porosity as a function of position in the direction of diffusion.     

Diffusive transport through compacted Na- and Ca-bentonite

The effect of exchangeable cation — Na⁺ and Ca ²⁺ — on the diffusive transport of I⁻, Sr ²⁺ and ³H (as HTO) in compacted bentonite was examined using a through-diffusion method. Total intrinsic diffusion coefficients, D_i, were determined from the steady-state flux of the diffusants through the clays, and apparent diffusion coefficients, D_a, were obtained from the time lag technique. The clays were compacted to a dry bulk density of 1.3 Mg/m³, and Na-bentonite was saturated with a solution of 100 mol NaCl/m3 and Ca-bentonite with one of 50 mol CaCl₂/m³. The D_i values for all diffusants are 2 to 6 times higher in the Ca- than Na-clay. We attribute this to the larger quasicrystal, or particle, size of Ca- compared to Na-bentonite. Hence, Ca-bentonite has a greater proportion of relatively large pores; this was confirmed by Hg intrusion porosimetry. This means the diffusion pathways in Ca-bentonite are less tortuous than those in Na-bentonite. Moreover, in some cases the effective porosity, or the porosity available for diffusive transport, may be greater in Ca-bentonite. The D_a values are inversely proportional to the distribution coefficients of the diffusants with the clays.     

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.     

Diffusion of tritiated water and Na through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and ²²Na⁺, considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test.The experimental data were inversely modelled applying an automated Marquardt–Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D_e, and the rock capacity factor, α. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K_d-values were found to be consistent with R_d-values measured in previous batch-sorption experiments.The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption.Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.