Evaluation of distribution coefficients for the prediction of strontium and cesium migration in a uniform sand

1982 ◽  
Vol 19 (1) ◽  
pp. 92-103 ◽  
Author(s):  
W. D. Reynolds ◽  
R. W. Gillham ◽  
J. A. Cherry
Keyword(s):  
Distribution Coefficient ◽  
Breakthrough Curves ◽  
Distribution Coefficients ◽  
Column Experiments ◽  
Advection Equation ◽  
Dispersion Models ◽  
Advection Dispersion ◽  
Liquid Phases ◽  
Long Tails ◽  
The Mathematical Model

The validity of using a distribution coefficient (Kd) in the mathematical prediction of strontium and cesium transport through uniform saturated sand was investigated by comparing measured breakthrough curves with curves of simulations using the advection-dispersion and the advection equations. Values for Kd were determined by batch equilibration tests and, indirectly, by fitting the mathematical model to breakthrough data from column experiments. Although the advection-dispersion equation accurately represented the breakthrough curves for two nonreactive solutes (chloride and tritium), neither it nor the advection equation provided close representations of the strontium and cesium curves. The simulated breakthrough curves for strontium and cesium were nearly symmetrical, whereas the data curves were very asymmetrical, with long tails. Column experiments with different pore-water velocities indicated that the shape of the normalized breakthrough curves was not sensitive to velocity. This suggests that the asymmetry of the measured curves was the result of nonlinear partitioning of the cations between the solid and liquid phases, rather than nonequilibrium effects. The results indicate that the distribution coefficient, when used in advection-dispersion models for prediction of the migration of strontium and cesium in field situations, can result in significant error.

scholarly journals Preselection of a sorption model based on a column test: the algorithm and an example of its application

2021 ◽  
Author(s):  
Marek Marciniak ◽  
Monika Okońska ◽  
Mariusz Kaczmarek
Keyword(s):  
Mathematical Model ◽  
Breakthrough Curve ◽  
Breakthrough Curves ◽  
Transport Processes ◽  
Column Experiments ◽  
Transport Parameters ◽  
Sorption Model ◽  
Advection Dispersion ◽  
Conservative Tracer ◽  
Reactive Tracer

AbstractIn order to describe the contamination of saturated porous media, it is necessary to find an appropriate mathematical model that includes processes occurring in aquifers, such as advection, dispersion, diffusion, and various kinds of sorption. The identification of parameters of those processes is possible through laboratory column experiments, which result in records of breakthrough curves for a conservative tracer and a reactive tracer. An algorithm leading to the preliminary selection of the mathematical model that best describes transport processes of the reactive tracer in the experimental column is proposed in this article. A study published previously presented a sensitivity analysis for an arbitrarily adopted variability of the transport parameters. The analysis involved examining changes in the shape of breakthrough curves caused by the alteration of each parameter value. Specially defined indicators called descriptors were proposed to quantitatively describe the breakthrough curves. Then, formulas were proposed to determine the percentage deviations of descriptors of the breakthrough curve obtained for the reactive tracer in relation to the descriptors of the breakthrough curve of the conservative tracer. In the work described in this article, the deviations are analyzed and an algorithm is proposed that allows the preselection of the most suitable sorption model out of the five discussed simple (one-site) and six hybrid (two-site) models. The algorithm can facilitate and accelerate the interpretation of column experiments of contaminant transport in a porous medium. An example is provided to illustrate the usability of the proposed algorithm.

Phosphorus transport in saturated slag columns: experiments and mathematical models

1996 ◽  
Vol 34 (1-2) ◽  
pp. 153-160 ◽  
Author(s):  
S. H. Lee ◽  
S. Vigneswaran ◽  
K. Bajracharya
Keyword(s):  
Mathematical Models ◽  
Sorption Capacity ◽  
Algal Blooms ◽  
Sandy Loam ◽  
Dynamic Condition ◽  
Water Environment ◽  
Breakthrough Curves ◽  
Column Experiments ◽  
Phosphorus Transport ◽  
Waste Products

Excessive phosphorus (P as orthophosphate) is one of the major pollutants in natural water that are responsible for algal blooms and eutrophication. P removal by slag is an attractive solution if the P sorption capacity of slag is significant. To design an efficient land treatment facility, basic information on the behaviour of P in the media-water environment is required. In this study, detailed column experiments were conducted to study the P transport under dynamic condition, and mathematical models were developed to describe this process. The column experiments conducted with dust and cake waste products (slag) from a steel industry as adsorbing indicated that they had higher sorption capacity of P than that of a sandy loam soil from North Sydney, Australia. P transport in the dust and cake columns exhibited characteristic S-shaped or curvilinear breakthrough curves. The simulated results from a dynamic physical nonequilibrium sorption model (DPNSM) and Freundlich isotherm constants satisfactorily matched the corresponding experimental breakthrough data. The mobility of P is restricted by the adsorbents and it is proportional to the sorption capacity of them.

Isomorphic Co-Crystallization of Ammonium and Rubidium Bromocarnallites

1994 ◽  
Vol 59 (8) ◽  
pp. 1815-1819 ◽  
Author(s):  
Christomir Christov ◽  
Christo Balarew ◽  
Stefka Tepavitcharova
Keyword(s):  
Distribution Coefficients ◽  
Mixed Crystals ◽  
Solubility Isotherm ◽  
Continuous Series ◽  
Liquid Phases

The solubility isotherm of the system NH4Br.MgBr2.6 H2O - RbBr.MgBr2.6 H2O - H2O has been investigated at 75 °C and formation of a continuous series of mixed crystals is established. The factors determining the values of the distribution coefficients of the components between the crystalline and liquid phases are discussed.

Consideration on modeling of Nb sorption onto clay minerals

2020 ◽  
Vol 108 (11) ◽  
pp. 873-877
Author(s):  
Tetsuji Yamaguchi ◽  
Saki Ohira ◽  
Ko Hemmi ◽  
Logan Barr ◽  
Asako Shimada ◽  
...  
Keyword(s):  
Distribution Coefficient ◽  
Clay Minerals ◽  
Safety Assessment ◽  
Distribution Coefficients ◽  
Surface Species ◽  
Complex Species ◽  
Intermediate Depth ◽  
Speciation Model ◽  
Surface Phases ◽  
High Distribution Coefficient

AbstractSorption distribution coefficient (Kd) of niobium-94 on minerals are an important parameter in safety assessment of intermediate-depth disposal of waste from core internals etc. The Kd of Nb on clay minerals in Ca(ClO4)2 solutions were, however, not successfully modeled in a previous study. The high distribution coefficients of Nb on illite in Ca(ClO4)2 solutions were successfully reproduced by taking Ca–Nb–OH surface species into account. Solubility of Nb was studied in Ca(ClO4)2 solutions and the results were reproduced by taking an aqueous Ca–Nb–OH complex species, CaNb(OH)6+, into account in addition to previously reported Nb(OH)6− and Nb(OH)72−. Based on this aqueous speciation model, the Ca–Nb–OH surface species responsible for the sorption of Nb on illite in Ca(ClO4)2 solutions was presumed to be X_OCaNb(OH)6. Although uncertainties exist in the speciation of aqueous Ca–Nb–OH species, the result of this study proposed a possible mechanism for high distribution coefficient of Nb on illite in Ca(ClO4)2 solutions. The mechanism includes Ca–Nb–OH complex formation in aqueous, solid and surface phases.

An Overview of Stochastic Tools for Modeling Transport of Tracers in Heterogeneous Media

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Spatial Variability ◽  
Heterogeneous Media ◽  
Breakthrough Curves ◽  
Velocity Shear ◽  
Numerical Dispersion ◽  
Complex Flow ◽  
Advection Dispersion ◽  
Arbitrary Dimensions ◽  
Flow Configurations ◽  
Small Solute

Spatial variability and the uncertainty in characterizing the flow domain play an important role in the transport of contaminants in porous media: they affect the pathlines followed by solute particles, the spread of solute bodies, the shape of breakthrough curves, the spatial variability of the concentration, and the ability to quantify any of these accurately. This chapter briefly reviews some basic concepts which we shall later employ for the analysis of solute transport in heterogeneous media, and also points out some issues we shall address in the subsequent chapters. Our exposition in chapters 8-10 on contaminant transport is built around the Lagrangian and the Eulerian approaches for analyzing transport. The Eulerian approach is a statement of mass conservation in control volumes of arbitrary dimensions, in the form of the advection-dispersion equation. As such, it is well suited for numerical modeling in complex flow configurations. Its main difficulties, however, are in the assignment of parameters, both hydrogeological and geochemical, to the numerical grid blocks such that the effects of subgrid-scale heterogeneity are accounted for, and in the numerical dispersion that occurs in advection-dominated flow situations. Another difficulty is in the disparity between the scale of the numerical elements and the scale of the samples collected in the field, which makes the interpretation of field data difficult. The Lagrangian approach focuses on the displacements and travel times of solute bodies of arbitrary dimensions, using the displacements of small solute particles along streamlines as its basic building block. Tracking such displacements requires that the solute particles do not transfer across streamlines. Since such mass transfer may only occur due to pore-scale dispersion, Lagrangian approaches are ideally suited for advection-dominated situations. Let us start by considering the displacement of a small solute body, a particle, as a function of time. “Small” here implies that the solute body is much smaller than the characteristic scale of heterogeneity. At the same time, to qualify for a description of its movement using Darcy’s law, the solute body also needs to be larger than a few pores. The small dimension of the solute body ensures that it moves along a single streamline and that it does not disintegrate due to velocity shear.

scholarly journals Cadmium distribution coefficeints and Cd transport in structured soils

2011 ◽  
Vol 48 (No. 3) ◽  
pp. 96-100 ◽  
Author(s):  
Ľ. Lichner ◽  
A. Čipáková
Keyword(s):  
Distribution Coefficient ◽  
Distribution Coefficients ◽  
Equilibrium Distribution Coefficient ◽  
Loamy Sand Soil ◽  
Structured Soils ◽  
Cadmium Transport ◽  
Batch Technique ◽  
The Matrix ◽  
Loam Soil ◽  
Cd Transport

In the case of cadmium transport via soil macropores, the short-term duration of an interaction between the reactive solute in aqueous phase and soil, as well as cadmium precipitation or adsorption on particles < 10–5 m should be taken into account. Two distribution coefficients are proposed for predicting the cadmium transport in a structured soil: the matrix distribution coefficient Kdm, equal to the equilibrium distribution coefficient Kdeq and estimated using the conventional batch technique, and the macropore distribution coefficient KdM, estimated using the modified batch technique. It was found that the conventional approach (using the coefficient Kdeq only) would underestimate a penetration of the part of Cd transported in the macropores about 255-times in the loamy-sand soil in Kalinkovo, 20-times in the loam soil in Macov, and 122-times in the clay soil in Jurová in comparison with the approach proposed in this study.

scholarly journals Electrical Phenomena accompanying the Phase Change of Dilute KCl Solutions into Single Crystals of Ice

1970 ◽  
Vol 9 (56) ◽  
pp. 269-277 ◽  
Author(s):  
T. E. Osterkamp ◽  
A. H. Weber
Keyword(s):  
Growth Rate ◽  
Liquid Phase ◽  
Phase Change ◽  
Distribution Coefficient ◽  
Single Crystals ◽  
Phase Distribution ◽  
Distribution Coefficients ◽  
Solute Distribution ◽  
Ice Crystals ◽  
Apparent Diffusion Coefficients

The Workman-Reynolds effect was investigated during the phase change of dilute (about 2 × 10-4 N) KCl solutions into single crystals of ice. The ice crystals were oriented with the c-axes either parallel or perpendicular to the growth direction. The solute distribution in the liquid phase. near the interface (within 10 mm), was obtained with a wire-type conductivity cell. For a crystal growth rate 8.8 μm/s the freezing potentials were + 10.0 V and + 6.0 V and the specific charge séparations were 1.3 ± 0 1 × 10-6 C/g of ice and 1 4 ± 0.1 × 10-6 C/g of ice for growth parallel and perpendicular. Respectively, to the c-axes of the ice crystals . The equilibrium solute distribution coefficient was found to be 4 × 10-3 for KCl solutions for both crystal orientations. An “apparent” (because of convection in the liquid phase) distribution coefficient ranged from 0.031- 0.074. The “apparent” diffusion coefficients ranged from 1.3–4.9 × 10-3 mm2/s and varied linearly with growth rate. The ionic distribution coefficients. K+ and K-, were approximately K+ - K- = - 2 × 10-5 and K+ + K - = 8 × 10-3 for the KCl solutions.

scholarly journals Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography

2020 ◽  
Vol 117 (38) ◽  
pp. 23443-23449 ◽  
Author(s):  
Sharul Hasan ◽  
Vahid Niasar ◽  
Nikolaos K. Karadimitriou ◽  
Jose R. A. Godinho ◽  
Nghia T. Vo ◽  
...  
Keyword(s):  
Solute Transport ◽  
High Speed ◽  
Three Dimensional ◽  
Concentration Field ◽  
Solute Concentration ◽  
Breakthrough Curves ◽  
Pore Scale ◽  
X Ray ◽  
Long Tails ◽  
Computed Microtomography

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

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