Apparent Dispersion Coefficients Research Articles

Time-dependent dispersion coefficients for the evolution of displacement fronts in heterogeneous porous media

We present an approach for quantifying displacement fronts in heterogeneous porous media based on the concept of time-dependent apparent dispersion coefficients. The concept of constant asymptotic macrodispersion generally overestimates the area swept by a displacement front and leads to unrealistic upstream dispersion. We show that the large-scale front spreading can be captured by a one-dimensional advection–dispersion equation that is parameterized by a suitably chosen temporally evolving dispersion coefficient. For purely advective front spreading, we derive an analytical expression based on a predictive continuous time random walk approach, which applies to highly heterogeneous porous media. This analysis elucidates the variability of solute travel times as the key longitudinal spreading mechanism. It shows that the evolution of dispersion can be captured as the sum of exponentials that decay on two dominant time scales. In a particle-based picture, these scales mark the short time at which transported particles start exploring the flow variability and the large time at which the slowest particles start decorrelating their transport velocity. Based on these insights, we propose a heuristic formula that accounts for the impact of local-scale dispersion as an additional decorrelation mechanism. The heuristic expression for the longitudinal dispersion coefficient captures solute spreading for a broad range of Péclet numbers and heterogeneity variances. The proposed approach is tested against direct numerical simulations. It provides a robust and fast method for quantifying the evolution of displacement fronts in heterogeneous porous media with possible applications, for example, in groundwater contamination modelling, underground gas storage, and geothermal energy production.

Sequential Extraction of 239+240Pu and the Vertical Distribution of 239+240Pu, 137Cs, and Heavy Metals in Chang-Bai Mountains’ Grassland Soil

To establish a 239+240Pu, 137Cs, and heavy metal reference soil site in Northeast China, three grassland soil cores were collected from the Lao-Ye-Ling Mountain, which is a branch of the Chang-Bai Mountains. The activities were in the range of 0.041–2.752 mBq/g for 239+240Pu and in the range of 0.2–57.6 mBq/g for 137Cs. The 240Pu/239Pu atomic ratios were 0.161–0.186, showing that 239+240Pu in the study area originated from the global fallout. Also, 239+240Pu, 137Cs, and excess 210Pb were enriched in the surface soil. The convective–dispersion equation model provided the lower apparent dispersion coefficients (D) and apparent convection velocities (v) for both 239+240Pu and 137Cs. The soil erosion rate in this study area was estimated by an erosion model, which was lower than that in the other area of Northeast China. 239+240Pu in the different soil fractions was analyzed by a sequential extraction method, and the result showed that 239+240Pu was mainly adsorbed by Fe/Mn oxides and their associated organic matter (NOMFe/Mn-oxides fraction). Except for Fe, all other heavy metals from the anthropogenic source were enriched in the surface soil. The pollution level of heavy metals in this study area was lower. In general, the alpine grassland soil of the Lao-Ye-Ling Mountain can be used as a reference soil site to study environmental pollution and soil erosion and provided some reference baselines for future multidisciplinary studies in Northeast Asia.

A new experimental method for comparing solvents in steam-solvent coinjection for bitumen recovery under controlled thermodynamic conditions

Solvent-aided steam-assisted gravity drainage (SA-SAGD) involves the interplay between phase behavior and fluid flow near the edge of a steam chamber, which affects the mixing of solvent with bitumen. The mixing of solvent with bitumen (i.e., dispersion) results in dilution of the bitumen and can improve the energy efficiency of SAGD. However, it is often difficult to analyze this complex interplay through large-scale steam injection experiments because of the transient chamber-edge thermodynamic conditions.This paper presents an experimental program that compares the bitumen gravity drainage with steam injection (SAGD) and solvent-steam co-injection (SA-SAGD) under controlled thermodynamic conditions. In addition to SAGD as the base case, two sets of SA-SAGD were performed with 20 mol% C4 and 10 mol% C8 in the coinjected vapor at 3500 kPa. The experiments used a sand-pack of 3-inch diameter and 15-inch length, which was placed in a 25-L cylindrical pressure vessel. The sand-pack was surrounded by one-inch annular space, into which the vapor phase was injected under controlled pressure, temperature, and composition. Oil production and temperature profiles inside and outside the sand-pack were recorded for all experiments. Excavated samples from the sand-pack were analyzed after the experiments.The total recovery factors for SAGD, C4-SAGD, and C8-SAGD were 78%, 84%, and 89%, respectively. The recovery factors at 1 h for SAGD, C4-SAGD, and C8-SAGD were 71%, 80%, and 85%, respectively. The peak oil rate was 9.8 cm3/min with SAGD, 14.6 cm3/min with C4-SAGD, and 31.3 cm3/min with C8-SAGD. The SA-SAGD cases resulted in markedly better results than the SAGD case, and C8-SAGD yielded more rapid oil drainage than C4-SAGD.The SAGD experimental data were history-matched using a numerical simulation model. Based on the calibrated numerical model, the SA-SAGD experimental data were history-matched by adjusting the dispersion coefficient to model the mixing between the solvent and bitumen. The apparent dispersion coefficients for C4 and C8 in bitumen were determined to be 0.012 m2/day and 0.093 m2/day, respectively. The experimental program verified in this research offers a way to systematically compare different solvents for SA-SAGD with their quantifiable dispersion coefficients under given chamber conditions.

First study of 237Np in Chinese soils: Source, distribution and mobility in comparison with plutonium isotopes

In this study, the distribution and migration of 237Np and 239+240Pu in soils in the vicinity (<5 km) of Qinshan and Tianwan Nuclear Power Plants in China were studied, which is the first specific study of global fallout 237Np in Chinese soils. The 237Np and 239+240Pu concentrations in surface soils showed large spatial inhomogeneity. A remarkable 239+240Pu concentration (4.783 mBq/g) was observed in a surface soil near Qinshan NPP and stands for the ever reported highest value in the Chinese soils. The inventories of 239+240Pu in two Qinshan and Tianwan soil cores were estimated to be 128.8 Bq/m2 and 121.0 Bq/m2, respectively; while the 237Np inventories were 0.039 Bq/m2 and 0.035 Bq/m2 at these sites, respectively. The 240Pu/239Pu atomic ratios in these soils indicated that the global fallout is the main source of Pu in these regions. However, the non-isotopic 237Np/239Pu atomic ratio in environmental soil is not a sensitive indicator for source identification. Furthermore, we conducted pilot study on the migration behaviors of 237Np and 239+240Pu in soil core at Qinshan site with the Convection-Dispersion Equation (CDE) model. The obtained apparent dispersion coefficients of 237Np (2.82 ± 2.06 cm2/y) was 5 times higher than that of 239+240Pu (0.57 ± 0.16 cm2/y), proving that 237Np has stronger migration ability than Pu isotopes in the Qinshan soil. Finally, we predicted that with the increase of migration time, both 237Np and 239+240Pu concentration in the soil will gradually become more evenly distributed among different soil layers due to the dominant dispersion effects.

Distinctive distributions and migrations of 239+240Pu and 241Am in Chinese forest, grassland and desert soils

The vertical distributions and downward migrations of the global fallout derived 239+240Pu and 241Am in diverse types of Chinese soils (forest, grassland and desert) were studied. The mean 239+240Pu and 241Am activity concentrations in the investigated soil cores were 0.28–0.69 mBq/g and 0.13–0.37 mBq/g, respectively, while the accumulative inventories were 61.53–138.99 Bq/m2 for 239+240Pu and 28.29–61.05 Bq/m2 for 241Am. The convection-dispersion equation (CDE) was used to calculate the migration parameters of 239+240Pu and higher apparent dispersion coefficients (D) were observed for the acidic forest soils compared with the alkaline grassland and desert soils; meanwhile a compartment model was employed to compare the migration of 239+240Pu and 241Am in successive soil layers which showed that the migration behaviors of 239+240Pu and 241Am were rather similar; both velocities were less than 0.3 cm/y in diverse types of soils and these findings were compatible with those of short-term laboratory simulation experiments in China.

Transport of dissolved organic matter in Boom Clay: Size effects

A coupled experimental-modelling approach was developed to evaluate the effects of molecular weight (MW) of dissolved organic matter (DOM) on its transport through intact Boom Clay (BC) samples. Natural DOM was sampled in-situ in the BC layer. Transport was investigated with percolation experiments on 1.5cm BC samples by measuring the outflow MW distribution (MWD) by size exclusion chromatography (SEC). A one-dimensional reactive transport model was developed to account for retardation, diffusion and entrapment (attachment and/or straining) of DOM. These parameters were determined along the MWD by implementing a discretisation of DOM into several MW points and modelling the breakthrough of each point. The pore throat diameter of BC was determined as 6.6–7.6nm. Below this critical size, transport of DOM is MW dependent and two major types of transport were identified. Below MW of 2kDa, DOM was neither strongly trapped nor strongly retarded. This fraction had an averaged capacity factor of 1.19±0.24 and an apparent dispersion coefficient ranging from 7.5×10−11 to 1.7× 10−11m2/s with increasing MW. DOM with MW>2kDa was affected by both retardation and straining that increased significantly with increasing MW while apparent dispersion coefficients decreased. Values ranging from 1.36 to 19.6 were determined for the capacity factor and 3.2×10−11 to 1.0×10−11m2/s for the apparent dispersion coefficient for species with 2.2kDa<MW<9.3kDa. Straining resulted in an immobilisation of in average 49±6% of the injected 9.3kDa species. Our findings show that an accurate description of DOM transport requires the consideration of the size effects.

Effect of temperature on the equilibrium and kinetics of galactose, glucose, and lactose adsorption on a cation exchanger

AbstractGalacto-oligosaccharides are typically produced by an enzymatic reaction when the post-reaction mixture contains considerable amounts of lactose and glucose and a smaller amount of galactose. In order to develop a process of chromatographic removal of saccharide impurities, adsorption equilibria and kinetics of these di- and monosaccharides were investigated for Diaion UBK 530, an industrialgrade strong cation-exchanger in the Na+ form. Frontal chromatographic experiments were carried out in the temperature range of 30–70°C and a broad interval of saccharide concentrations up to 350 g L−1. Breakthrough curves were described using the equilibrium-dispersive model with the linear adsorption isotherm. Both the distribution and the axial dispersion coefficient values depended on the saccharide molecule type and size. No significant effect of temperature or concentration on the distribution coefficient was observed. The apparent dispersion coefficients of all saccharides exhibited some decrease with the temperature, which was caused by the decrease of the intraparticle mass transfer resistance. An analysis showed that both the intraparticle mass transfer and the axial dispersion had a significant influence on the front dispersion.

CO2 sequestration for enhanced gas recovery: New measurements of supercritical CO2–CH4 dispersion in porous media and a review of recent research

The enhanced recovery of natural gas by the injection and sequestration of CO2 is an attractive scenario for certain prospective field developments if the risks of gas contamination or early CO2 breakthrough can be assessed reliably. Simulations of enhanced gas recovery (EGR) scenarios require accurate dispersion parameters at reservoir conditions to quantify the size of the miscible CO2–CH4 displacement front; several experimental studies using core-flooding equipment aimed at measuring such parameters have been reported over the last decade. However, such measurements are particularly challenging and the data produced are generally afflicted in their repeatability by limited experimental control and in their accuracy by systematic errors such as gravitational and core-entrance/exit effects. We review here the existing experimental data pertaining to EGR by CO2 sequestration and also report new measurements of longitudinal CO2–CH4 dispersion coefficients at temperatures of 40–80°C, pressures of 8–12MPa and interstitial velocities of 0.05–1.13mms−1 [14.2–320ftday−1] in 5–10cm long sandstone cores with permeabilities of 12 and 460mD. The core-floods were conducted in both a horizontal and vertical orientation, with significant gravitational effects observed for low velocity floods in horizontal cores with high permeabilities. We also analyzed the effects of tubing and core entrance/exit effects on the measurements and found that the latter resulted in apparent dispersion coefficients up to 63% larger than would be due to the core alone. Our results indicate that dispersivities for CO2–CH4 at these supercritical conditions are less than 0.001m, which indicates that excessive mixing will not occur in EGR scenarios in the absence of conformance effects such as heterogeneity coupled with injection well pattern. Inclusion of such conformance effects is essential for detailed reservoir simulation.

画像処理による油輸送の定量化手法の開発とホットウォーターフラッシング実験への適用

Hot water flushing experiments in a two-dimensional sandbox (35 cm × 20 cm × 1 cm) were conducted using dyed salad oil in single and two-layered porous formations under saturated conditions. Based on a calibration relation between the dye concentration and the corresponding pixel brightness an image processing technique in conjunction with spatial moments was developed to quantify not only the spatial distribution of oil but the apparent retardation and dispersion coefficients both in longitudinal and lateral directions. The increase of flooding water temperature resulted in accelerated downward movement of oil because of the reduced viscosity at elevated temperatures. The results also revealed that the variation of the apparent lateral dispersion coefficient depended on the oil saturation within a pore space and exhibited an increasing tendency in a smaller size porous material due to the difference of intrinsic permeability.

Electrokinetic Study of Migration of Anions, Cations, and Water in Water-Saturated Compacted Sodium Montmorillonite

Electromigration studies of 36Cl− ions and 22Na+ ions, and electro-osmosis of water traced with HTO and H2 18O were conducted with water-saturated compacted sodium montmorillonite having dry densities from 0.8 to 1.6 Mg/m3. The mobilities and dispersivities for each species were obtained from the apparent electromigration velocities and hydrodynamic dispersion coefficients, respectively. When corrected by water flow, the apparent diffusion coefficients of Cl− ions obtained from the Einstein relation are in good agreement with the coefficients obtained from an earlier conventional diffusion experiment in the high dry densities (above 1.3 Mg/m3,). This result suggests that the migration pathways of Cl− ions are nearly identical to those of water above 1.3 Mg/m3. The former diffusion coefficient is smaller than the latter in the low dry densities (below 1.3 Mg/m3), suggesting that Cl− ions migrate in the region distant from the montmorillonite sheets. In contrast, for Na+ ions, the obtained Da values without water flow correction are in good agreement with conventional values at all dry densities. This suggests that Na+ ions migrate mainly in the interlayer and the vicinity of montmorillonite sheets. The dispersivities increase with increasing dry densities for all species. This corresponds to a geometrical complexity that increases with increasing dry density.

Electrokinetic Study of Migration of Anions, Cations, and Water in Water-Saturated Compacted Sodium Montmorillonite

Electromigration studies of 36Cl− ions and 22Na+ ions, and electro-osmosis of water traced with HTO and H2 18O were conducted with water-saturated compacted sodium montmorillonite having dry densities from 0.8 to 1.6 Mg/m3. The mobilities and dispersivities for each species were obtained from the apparent electromigration velocities and hydrodynamic dispersion coefficients, respectively. When corrected by water flow, the apparent diffusion coefficients of Cl− ions obtained from the Einstein relation are in good agreement with the coefficients obtained from an earlier conventional diffusion experiment in the high dry densities (above 1.3 Mg/m3,). This result suggests that the migration pathways of Cl− ions are nearly identical to those of water above 1.3 Mg/m3. The former diffusion coefficient is smaller than the latter in the low dry densities (below 1.3 Mg/m3), suggesting that Cl− ions migrate in the region distant from the montmorillonite sheets. In contrast, for Na+ ions, the obtained Da values without water flow correction are in good agreement with conventional values at all dry densities. This suggests that Na+ ions migrate mainly in the interlayer and the vicinity of montmorillonite sheets. The dispersivities increase with increasing dry densities for all species. This corresponds to a geometrical complexity that increases with increasing dry density.

Influence of Viscous Friction Heating on the Efficiency of Columns Operated under Very High Pressures

When columns packed with very fine particles are operated at high mobile phase velocities, the friction of the mobile phase percolating through the column bed generates heat. This heat dissipates along and across the column and axial and radial temperature gradients appear. The wall region of the column tends to be cooler than its center, and due to the influence of temperature on the mobile phase viscosity and on the equilibrium constant of analytes, the band velocity is not constant across the column. This radial heterogeneity of the temperature distribution across the column contributes to band broadening. This phenomenon was investigated assuming a cylindrically symmetrical column and using the general dispersion theory of Aris, which relates the height equivalent to the theoretical plate (HETP) contribution due to a radial heterogeneity of the column to the radial distribution of the linear velocities of a compound peak and to the radial distribution of its apparent dispersion coefficients in the column bed. The former is known from the temperature gradient across the column, the temperature dependencies of the mobile phase viscosity, and the retention factor of the compound. The latter is derived from the known expression of the transverse reduced HETP equation for the column. The values of the HETP calculated with the Aris model and a classical HETP equation were compared to those measured on a 2.1 x 50 mm Acquity BEH-C(18) column, run at flow rates of 0.6, 0.95, 1.30, and 1.65 mL/min, with pure acetonitrile as the mobile phase and naphtho[2,3-a]pyrene as the retained compound. These two sets of data are in generally good agreement, although the experimental values of the HETP tend to increase faster with increasing mobile phase velocity than the calculated values.

Anisotropic effective medium solutions of head and velocity variance to quantify flow connectivity

Most methods for upscaling flow and transport in heterogeneous media from the measurement scale to the simulation scale for field applications generally focus on the prediction of values of effective permeability and apparent dispersion coefficients. Although typically considered as secondary data, measures of head variance σ ϕ 2 and velocity variance σ qx 2 also contain valuable information on the level of heterogeneity of the hydraulic conductivity ( K) distribution of the soil. In particular, we investigate the suitability of σ ϕ 2 and σ qx 2 to yield insight into the potential occurrence of flow barriers and preferential pathways, which significantly affect flow connectivity. Before the application of complex numerical simulators, a proper understanding of the actual link between head and velocity variance, and the spatial distribution of K can be obtained using closed-form solutions. In this paper, semi-analytical expressions of effective permeability, head variance, and velocity variance are derived for saturated flow in two-dimensional anisotropic porous media. The expressions are obtained using the methodology initially proposed by Dagan [Dagan G. Models of groundwater flow in statistically homogeneous porous formations. Water Resour Res 1979;15(1):47–63] for isotropic heterogeneous formations. The solutions are illustrated in the case of binary heterogeneous media and compared to results from numerical simulations of steady-state flow in random K fields. It is found that the self-consistent solution generally yields relatively poor results when applied to the prediction of head statistics, while both longitudinal and transverse velocity variance are correctly predicted in all cases. The results of the numerical simulations are also used to illustrate the link between σ ϕ 2 , σ qx 2 , and flow connectivity. Although head variance is not a stationary property of two-dimensional flow fields, and hence might not exactly represent an intrinsic property of flow such as connectivity, it is found that σ ϕ 2 is negatively correlated to effective permeability K e , x for poorly connected K fields. On the contrary, σ qx 2 is found to be positively correlated to K e , x for all levels of connectivity. Therefore, the results suggest that these statistics of the flow field could be used to quantify flow connectivity when measures of other indicators are not available.

Migration Behavior of Plutonium in Compacted Bentonite Under Reducing Condition Using Electromigration

AbstractCarbon steel is one of the candidate overpack materials for high-level waste disposal and is expected to assure complete containment of vitrified waste glass during an initial period of 1000 years in Japan. Carbon steel overpack will be corroded by consuming oxygen introduced by repository construction after closure of repository and then will keep the reducing environment in the vicinity of repository. The migration of iron corrosion products through the buffer material will affect migration of redox-sensitive radionuclides. Therefore the authors have carried out electromigration experiments with source of iron ions supplied by anode corrosion of iron coupons attached to compacted bentonite. Authors tried to use plutonium in this experimental configuration to obtain the knowledge of migration behavior of actinides. Authors also used cesium as reference. The concentrations of iron and sodium showed nearly complementary distributions. It is expected that iron ion could migrate as ferrous ion through the interlayer of montmorillonite replacing exchangeable sodium ions in the interlayer. Concentration profiles of plutonium in bentonite grew as time supplying electric potential as long as 168 h. Plutonium migrated from the iron anode toward cathode as deeper than 1 mm of the interior of bentonite even in 48 h, though plutonium could not diffuse 1 mm for 2 years. On the other hand, profiles of cesium seemed to be controlled by ordinary diffusion because of large diffusion coefficient of cesium in bentonite as large as 10$^{-12}$ m$^{2}$/s. Drift of the cesium profile by electric potential gradient could be observed clearly after 240 h at individual experiment for cesium. Apparent dispersion coefficients of plutonium were calculated from the profiles and were as large as 10$^{-13}$ m$^{2}$/s. Since plutonium migration was accelerated by electric potential, plutonium chemical species would have positive charge and were estimated as PuOH$^{2+}$ or PuCl$^{2+}$ by the thermodynamic calculation. Thus this experiment can provide a diffusion field for cations under a reducing condition with ferrous ions in water-saturated bentonite.

Migration Behavior of Cesium in Compacted Bentonite Under Reducing Conditions Using Electromigration

ABSTRACTCarbon steel overpack will be corroded by consuming oxygen introduced by repository construction after closure of repository and then will keep the reducing environment in the vicinity of repository. The migration of iron corrosion products through the buffer material will affect migration of redox-sensitive radionuclides. Therefore the authors have carried out electromigration experiments with source ofiron ions supplied by anode corrosion of iron coupons in compacted bentonite. However, their migration behavior was complex and difficult to explain. Thus, authors tried to use cesium, whose migration behavior is well known, inthis experimental configuration to obtain knowledge of the migration behavior of cations. The concentrationsof iron and sodium showed nearly complementary distributions. It is expected that iron ion could migrate as ferrous ion through the interlayer of montmorillonite replacing exchangeable sodium ions in the interlayer. On the other hand, cesium profiles seemed to be controlled by ordinary diffusion. Drift of the cesium profile by electric potential gradient could be observed clearly only after 240 h. Apparent dispersion coefficients of cesium were calculated from the profiles and were in reasonable agreement with literature values of apparent diffusion coefficients. Thus this experiment can provide a diffusion field for cations under a reducing condition with ferrous ions in water-saturated bentonite. The effect of electro-osmotic flow on ion migration was negligibly small in this experiment because electro-osmotic flow was compensated by hydraulic pressure caused by the water content gradient developed in the specimen within 24h.

Large‐scale sandbox experiment on longitudinal effective dispersion in heterogeneous porous media

In heterogeneous media the breakthrough curves observed at single points may differ significantly from those integrated over a control plane. While standard macrodispersion describes the spread of concentration averaged over the entire cross section, effective dispersion quantifies the average spread in the locally observed breakthrough curves. We perform a conservative tracer test in a 14‐m‐long sandbox filled heterogeneously with four types of silica sand. The filling resembles natural heterogeneities including the distribution of facies and micro‐structures within the various sand types. We use fluorescein as tracer, which we measure at 126 measurement points directly within the porous medium and at 19 levels in the outlet of the domain. We use fiber‐optic probes with a point‐like measurement tip for fluorescence intensity measurements. From the second central temporal moments of the locally obtained breakthrough curves we compute apparent effective dispersion coefficients, and from the average over all probes within a measurement plane we derive apparent macrodispersion coefficients. The effective dispersion coefficient is about two thirds of the macrodispersion coefficient. Considering the typical length scales of the heterogeneities, the experimental findings are qualitatively in agreement with linear stochastic theory.

Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: convergence to an equivalent homogeneous porous medium

In this article, the quadrupole method is implemented in order to simulate the effects of heterogeneities on one dimensional advective and diffusive transport of a passive solute in porous media. Theoretical studies of dispersion in heterogeneous stratified media can bring insight into transport artefacts linked to scale effects and apparent dispersion coefficients. The quadrupole method is an efficient method for the calculation of transient response of linear systems. It is based here on the Laplace transform technique. The analytical solutions that can be derived by this method assists understanding of upscaled parameters relevant to heterogeneous porous media. First, the method is developed for an infinite homogeneous porous medium. Then, it is adapted to a stratified medium where the fluid flow is perpendicular to the interfaces. The first heterogeneous medium studied is composed of two semi-infinite layers perpendicular to the flow direction each having different transport properties. The concentration response of the medium to a Dirac injection is evaluated. The case studied emphasises the importance in the choice of the boundary conditions. In the case of a periodic heterogeneous porous medium, the concentration response of the medium is evaluated for different numbers of unit-cells. When the number of unit cells is great enough, depending on the transport properties of each layer in the unit cell, an equivalent homogeneous behaviour is reached. An exact determination of the transport properties (equivalent dispersion coefficient) of the equivalent homogeneous porous medium is given.

Vertical distribution of radionuclides in soil of a grassland site in Chernobyl exclusion zone

Five soil profiles from a site about 8 km SE of the Chernobyl NPP were investigated for the vertical distribution of radionuclides. The average 137Cs-inventory at the site is about 2.6 MBq/m 2 (reference date 1 May 1986). Apart from 137Cs, the following radionuclides have been identified (their activity ratios to 137Cs in brackets): 134Cs (0.537), 125Sb (0.068), 60Co (0.0022), 154Eu (0.016), 155Eu (0.020), 94gNb (9.5E-5), 239/240Pu (0.0088), 238Pu (0.040), 90Sr (0.30) and 241Am (0.011). Apparent vertical migration velocities are between 0.14 and 0.26 cm/a, apparent dispersion coefficients range from 0.02 to 0.13 cm 2/a. The rankings of the velocities v for different radionuclides are (Sr, Cs, Sb, Co, Pu)<Am<Eu and Sr<(Cs, Nb), for D, the following rankings have been found: (Nb, Sr, Cs)<Am<Eu, Cs<Sb and Nb<Co (all on p=0.1 level).

Axial dispersion during low Reynolds number Taylor-Couette flow: intra-vortex mixing effects

Tracer experiments were employed to study axial mass transport in a Taylor-Couette device with a radius ratio of 0.875. The inner cylinder was rotated (with the outer cylinder fixed) at circumferential Reynolds numbers ranging from 1.05 to 7.50 times the critical value for the onset of laminar Taylor vortex flow. Apparent axial dispersion coefficients were found by fitting a three parameter model to tracer-response data. The model consisted of a network of CSTRs (each with an associated exchange volume) connected in series. The CSTRs corresponded to the well mixed outer layers of the Taylor vortices; the exchange volumes represented poorly mixed vortex cores. For 1.05 ≤ Re Re c < 5.0 , the apparent axial dispersion coefficient increased nonmonotonically with increasing Reynolds numbers. At inner cylinder rotation rates Re Re c > 5.0 , the model recovered the commonly used discrete approximation of the one-dimensional diffusion equation.

Study of flow and hydrodynamic dispersion in a porous medium using pulsed–field–gradient magnetic resonance

This paper reports on the use of pulsed–field gradient (PFG) magnetic resonance (MR) techniques to obtain displacement and velocity spectra of steady–state, saturated flow through a column packed with glass beads. The displacement spectra obtained by PFG MR correspond to travel–distance probability–density functions (PDF) for initial conditions of a concentration impulse in a column with zero concentration. These spectra show strong dispersion–time dependence, and depart from Gaussian–shaped PDFs for short dispersion times. These data provide estimates of the dispersion–time dependence of transverse and longitudinal dispersion coefficients. The longitudinal dispersion coefficient reaches its long–time behaviour more slowly than the transverse coefficient; long–time values obtained from MR data agree well with those calculated using existing empirical correlations. A model based on three components of apparent velocities and dispersion coefficients is sufficient to describe the time dependence of displacement spectra for water flow through the bead column. The short–distance component arise because of convection–dispersion–diffusion processes within the narrow necks between particles. The long–distance component, on the other hand, represents a macroscopic convection–dispersion process. This study shows that PFG MR flow spectroscopy is a simple but potentially useful method for the investigation of flow and hydrodynamic dispersion in porous media, especially for time–dependent phenomena.