Immobile Regions Research Articles

Multicomponent reactive transport in multicontinuum media

Multicomponent reactive transport in aquifers is a highly complex process, owing to a combination of variability in the processes involved and the inherent heterogeneity of nature. To date, the most common approach is to model reactive transport by incorporating reaction terms into advection‐dispersion equations (ADEs). Over the last several years, a large body of literature has emerged criticizing the validity of the ADE for transport in real media, and alternative models have been presented. One such approach is that of multirate mass transfer (MRMT). In this work, we propose a model that introduces reactive terms into the MRMT governing equations for conservative species. This model conceptualizes the medium as a multiple continuum of one mobile region and multiple immobile regions, which are related by kinetic mass transfer processes. Reactants in both the mobile and immobile regions are assumed to always be in chemical equilibrium. However, the combination of local dispersion in the mobile region and the various mass transfer rates induce a global chemical nonequilibrium. Assuming this model properly accounts for transport of reactive species, we derive explicit expressions for the reaction rates in the mobile and immobile regions, and we study the impact of mass transfer on reactive transport. Within this framework, we observe that the resulting reaction rates can be very different from those that arise in a system governed by an ADE‐type equation.

Combined physical and chemical nonequilibrium transport model: Analytical solution, moments, and application to colloids

The transport of solutes and colloids in porous media is influenced by a variety of physical and chemical nonequilibrium processes. A combined physical–chemical nonequilibrium (PCNE) model was therefore used to describe general mass transport. The model partitions the pore space into “mobile” and “immobile” flow regions with first-order mass transfer between these two regions (i.e, “physical” nonequilibrium or PNE). Partitioning between the aqueous and solid phases can either proceed as an equilibrium or a first-order process (i.e, “chemical” nonequilibrium or CNE) for both the mobile and immobile regions. An analytical solution for the PCNE model is obtained using iterated Laplace transforms. This solution complements earlier semi-analytical and numerical approaches to model solute transport with the PCNE model. The impact of selected model parameters on solute breakthrough curves is illustrated. As is well known, nonequilibrium results in earlier solute breakthrough with increased tailing. The PCNE model allows greater flexibility to describe this trend; for example, a closer resemblance between solute input and effluent pulse. Expressions for moments and transfer functions are presented to facilitate the analytical use of the PCNE model. Contours of mean breakthrough time, variance, and spread of the colloid breakthrough curves as a function of PNE and CNE parameters demonstrate the utility of a model that accounts for both physical and chemical nonequilibrium processes. The model is applied to describe representative colloid breakthrough curves in Ottawa sands reported by Bradford et al. (2002). An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data. A considerably better description was provide by the simple CNE model but the best description, especially for the larger 3.2-µm colloids, was provided by the PCNE model.

Effects of rock fragments on water movement and solute transport in a Loess Plateau soil

Calcium carbonate concretions are present in the soil of the Loess Plateau as a result of pedogenesis. The presence of these small rock fragments can have a great impact on soil bulk density, structure and water storage properties, as well as on soil water movement and solute transport processes. We studied the effects of different gravimetric rock fragment contents in a soil ( R w) (0, 10, 20, 30, 40, 50, and 60%) on infiltration, saturated hydraulic conductivity ( K s) and solute transport. Both infiltration rates and the saturated hydraulic conductivity initially decreased with increasing rock fragment content to minimum values for R w = 40%, and then increased. The Peck–Watson and Bouwer–Rice equations predicted K s for low rock fragment contents but failed to forecast the observed trends. Cumulative infiltration over time was described well by a power function. Solute transport processes, determined using CaCl 2 as a tracer, were accurately described by both the convection–dispersion equation (CDE) and the two-region model (T-R) although the T-R model fitted the experimental data a little better than the CDE, which is possibly more convenient to use. When R w was about 40% solute transport parameters indicated that relatively more advection occurred in this mixture where immobile regions occupied the greatest proportion of the columns.

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law-based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.

Formation and Characterization of Fluid Lipid Bilayers on Alumina

Fluid lipid bilayers were deposited on alumina substrates with the use of bubble collapse deposition (BCD). Previous studies using vesicle rupture have required the use of charged lipids or surface functionalization to induce bilayer formation on alumina, but these modifications are not necessary with BCD. Photobleaching experiments reveal that the diffusion coefficient of POPC on alumina is 0.6 microm (2)/s, which is much lower than the 1.4-2.0 microm (2)/s reported on silica. Systematically accounting for roughness, immobile regions and membrane viscosity shows that pinning sites account for about half of this drop in diffusivity. The remainder of the difference is attributed to a more tightly bound water state on the alumina surface, which induces a larger drag on the bilayer.

Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site

We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity ( K) and porosity ( ϕ), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.

Structural Analysis of Transmembrane Halobacterial Tranceducer pHtrII by Multi-Dimensional High-Resolution Solid-State NMR

°Transmembrane protein pHtrII is a transducer which binds to phoborhodopsin. The light excitation of phoborhodopsin is transmitted into the cytoplasm through pHtrII to promote negative photoaxis. We studied uniformly 13 C, 15 N labeled 159residues pHtrII by high-resolution solid-state NMR. The pHtrII (1-159) was econstructed into the deuterated DMPC membranes. High-resolution solid-state 2D NMR was measured under magic-angle spinning at the 1 H resonance frequencies of 500, 600 and 700 MHz . At first, we have assigned 13 C signals of pHtrII (1-159) by using 13 C- 13 C spin diffusion under DARR at -40 o C.Intraresidue correlations across 1-2 bonds were observed at short mixing time. At a long mixing time of 200 ms, intra-residue C α correlations across 3-bonds were obtained. Most amino acids except Tyr and Pro were assigned. The DARR spectra were observed for immobile region of pHtrII. All 13 C signals could not be observed in these dipolar-coupling-based cross-polarization methods because of large-amplitude molecular motions at room temperature. We performed Jcoupling-based HC-INEPT and HCC-TOCSY experiments in order to obtain signals of mobile protein segments. Mobile protein segments make up about 70% of pHtrII (1-159). Many signals in mobile regions were observed in HC and HCC 2D spectra. 13 C and 1 H signals were assigned to amino acid groups were successful in mobile regions. The C α and CO chemical shifts indicate that pHtrII (1-159) mainly forms α -helix structure in lipid bilayer environment.

Non‐Fickian dispersion in porous media: 1. Multiscale measurements using single‐well injection withdrawal tracer tests

We present a set of single‐well injection withdrawal tracer tests in a paleoreef porous reservoir displaying important small‐scale heterogeneity. An improved dual‐packer probe was designed to perform dirac‐like tracer injection and accurate downhole automatic measurements of the tracer concentration during the recovery phase. By flushing the tracer, at constant flow rate, for increasing time duration, we can probe distinctly different reservoir volumes and test the multiscale predictability of the (non‐Fickian) dispersion models. First we describe the characteristics, from microscale to meter scale, of the reservoir rock. Second, the specificity of the tracer test setup and the results obtained using two different tracers and measurement methods (salinity‐conductivity and fluorescent dye–optical measurement, respectively) are presented. All the tracer tests display strongly tailed breakthrough curves (BTC) consistent with diffusion in immobile regions. Conductivity results, measured over 3 orders of magnitude only, could have been easily interpreted by the conventional mobile‐immobile (MIM) diffusive mass transfer model of asymptotic log‐log slope of −2. However, the fluorescent dye sensor, which allows exploring much lower concentration values, shows that a change in the log‐log slope occurs at larger time with an asymptotic value of −1.5, corresponding to the double‐porosity model. These results suggest that the conventional, one‐slope MIM transfer rate model is too simplistic to account for the real multiscale heterogeneity of the diffusion‐dominant fraction of the reservoir.

The Effects of Dual-Domain Mass Transfer on the Tritium−Helium-3 Dating Method

Diffusion of tritiated water (referred to as tritium) and helium-3 between mobile and immobile regions in aquifers (mass transfer) can affect tritium and helium-3 concentrations and hence tritium-helium-3 (3H/3He) ages that are used to estimate aquifer recharge and groundwater residence times. Tritium and helium-3 chromatographically separate during transport because their molecular diffusion coefficients differ. Simulations of tritium and helium-3 transport and diffusive mass transfer along stream tubes show that mass transfer can shift the 3H/3He age of the tritium and helium-3 concentration ([3H + 3He]) peak to dates much younger than the 1963 peak in atmospheric tritium. Furthermore, diffusive mass-transfer can cause the 3H/3He age to become younger downstream along a stream tube, even as the mean water-age must increase. Simulated patterns of [3H + 3He] versus 3H/3He age using a mass transfer model appear consistent with a variety of field data. These results suggest that diffusive mass transfer should be considered, especially when the [3H + 3He] peak is not well defined or appears younger than the atmospheric peak. 3H/3He data provide information about upstream mass-transfer processes that could be used to constrain mass-transfer models; however, uncritical acceptance of 3H/3He dates from aquifers with immobile regions could be misleading.

Effects of water content on reactive transport of 85Sr in Chernobyl sand columns

It is known that under unsaturated conditions, the transport of solutes can deviate from ideal advective–dispersive behaviour even for macroscopically homogeneous porous materials. Causes may include physical non-equilibrium, sorption kinetics, non-linear sorption, and the irregular distribution of sorption sites. We have performed laboratory experiments designed to identify the processes responsible for the non-ideality of radioactive Sr transport observed under unsaturated flow conditions in an Aeolian sandy deposit from the Chernobyl exclusion zone. Miscible displacement experiments were carried out at various water contents and corresponding flow rates in a laboratory model system. Results of our experiments have shown that breakthrough curves of a conservative tracer exhibit a higher degree of asymmetry when the water content decreases than at saturated water content and same Darcy velocity. It is possible that velocity variations caused by heterogeneities at the macroscopic scale are responsible for this situation. Another explanation is that molecular diffusion drives the solute mass transfer between mobile and immobile water regions, but the surface of contact between these water regions is small. At very low concentrations, representative of a radioactive Sr contamination of the pore water, sorption and physical disequilibrium dominate the radioactive Sr transport under unsaturated flow conditions. A sorption reaction is described by a cation exchange mechanism calibrated under fully saturated conditions. The sorption capacity, as well as the exchange coefficients are not affected by desaturation. The number of accessible exchange sites was calculated on the basis that the solid remained in contact with water and that the fraction of solid phase in contact with mobile water is numerically equal to the proportion of mobile water to total water content. That means that for this type of sandy soil, the nature of mineral phases is the same in advective and non-advective domains. So sorption reaction parameters can be estimated from more easily conducted saturated experiments, but hydrodynamic behaviour must be characterized by conservative tracer experiments under unsaturated flow conditions.

Una nueva interpretación cuantitativa de curvas de avance con mesetasy largos limbos de recesión a partir de ensayos de trazadoren el acuífero cárstico artesiano de Stuttgart, Alemania

In 1998 and 1999, two multi-tracer experiments were conducted in the artesian karst aquifer of the mineral springs of Stuttgart, Germany. The breakthrough curves (BTCs) monitored at the springs showed very long tails or developed plateau-like concentration levels for more than 200 days. Initially, this observation was qualitatively explained by exchange between cavities with stagnant water and the active conduits. Since then, a new analytical solution for tracer transport in karst aquifers has become available, the “two-region non-equilibrium model” (2RNE), which assumes the presence of mobile and immobile fluid regions, and mass transfer between these two regions. The experiments were thus revisited, and it was possible to provide a more quantitative explanation of the observed behaviour. The new model simulated all BTCs very well, thus confirming the earlier qualitative explanation. The prolonged BTCs can be attributed to intermediate storage in cavities containing quasi-immobile groundwater, and slow release into active fractures and conduits. The results also demonstrate that karst aquifers are not always fast-flushing systems, but contaminants can sometimes remain in immobile fluid regions for long periods.

Transport and fate of bacteria in porous media: Coupled effects of chemical conditions and pore space geometry

Experimental and theoretical studies were undertaken to explore the coupled effects of chemical conditions and pore space geometry on bacteria transport in porous media. The retention of Escherichia coli D21g was investigated in a series of batch and column experiments with solutions of different ionic strength (IS) and ultrapure quartz sand. Derjaguin–Landau–Verwey–Overbeek (DLVO) calculations and results from batch experiments suggested that bacteria attachment to the sand surface was negligible when the IS was less than or equal to 50 mM. Breakthrough data from column experiments showed significant cell retention and was strongly dependent on the IS. This finding indicates that cell retention was dependent on the depth of the secondary energy minimum which increases with IS. When the IS of the influent bacteria‐free solution was decreased to 1 mM, only a small fraction of the retained bacteria was released from the column. The remaining retained bacteria, however, were recovered from the sand, which was excavated from the column and suspended in a cell‐free electrolyte having the original IS. These observations suggest that the solution chemistry is not the only parameter controlling bacteria retention in the porous media. Computational simulations of flow around several collector grains revealed the retention mechanism, which is dependent on both the solution chemistry and the pore space geometry. Simulations demonstrate that the pore space geometry creates hydrodynamically disconnected regions. The number of bacterial cells that may be transported to these relatively “immobile” regions will theoretically be dependent on the depth of the secondary energy minimum (i.e., the IS). Once bacteria are trapped in these immobile regions, reduction of the secondary energy minimum does not necessarily release the cells owing to hydrodynamic constraints.

Monitoring Protein Conformation along the Pathway of Chaperonin-Assisted Folding

The GroEL/GroES chaperonin system mediates protein folding in the bacterial cytosol. Newly synthesized proteins reach GroEL via transfer from upstream chaperones such as DnaK/DnaJ (Hsp70). Here we employed single molecule and ensemble FRET to monitor the conformational transitions of a model substrate as it proceeds along this chaperone pathway. We find that DnaK/DnaJ stabilizes the protein in collapsed states that fold exceedingly slowly. Transfer to GroEL results in unfolding, with a fraction of molecules reaching locally highly expanded conformations. ATP-induced domain movements in GroEL cause transient further unfolding and rapid mobilization of protein segments with moderate hydrophobicity, allowing partial compaction on the GroEL surface. The more hydrophobic regions are released upon subsequent protein encapsulation in the central GroEL cavity by GroES, completing compaction and allowing rapid folding. Segmental chain release and compaction may be important in avoiding misfolding by proteins that fail to fold efficiently through spontaneous hydrophobic collapse.

Incorporating Aqueous Reaction Kinetics and Biodegradation into TOUGHREACT: Applying a Multiregion Model to Hydrobiogeochemical Transport of Denitrification and Sulfate Reduction

The need to consider aqueous and sorption reaction kinetics and microbiological processes arises in many subsurface problems. By adding these processes to the TOUGH family code, more complex problems can be addressed that involve multiphase fluid and heat flow, and geochemical interaction. This paper presents a formulation for incorporating kinetic rates among primary species into mass‐balance equations. The space discretization used is based on a flexible integral finite difference approach that uses irregular gridding to model biogeologic structures. A general multiregion model for hydrological transport interacted with microbiological and geochemical processes is proposed. A one‐dimensional reactive transport problem with kinetic biodegradation and sorption was used to test the enhanced simulator, which involves the processes that occur when a pulse of water containing nitrylotriacetate (NTA) and cobalt is injected into a column. The current simulation results agree very well with those obtained with other simulators. The applicability of this general multiregion model was validated by results from a published column experiment of denitrification and sulfate reduction. The matches with measured nitrate and sulfate concentrations were adjusted with the interfacial area between mobile and immobile regions. Results suggest that TOUGHREACT not only is useful interpretative tool for biogeochemical experiments but also can produce insight into processes and parameters of microscopic diffusion and their interplay with biogeochemical reactions.

Temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media

Temporal moment equations are generalized for transport under linear mass transfer, which has been used to model a broad range of small‐scale processes: kinetic sorption, diffusion into immobile regions, and transport through heterogeneous aquifers. Solving the moment equations, which are formally identical to steady state transport equations, is computationally more efficient than evaluating the temporal moments by integrating the transient flux concentrations. We derive recursive relations for the moments of the flux concentration, which involve the moments of the memory function but do not dependent on its shape. It turns out that two mass transfer models have the same kth temporal moment if the moments of order lower than k are equal. Particularly, the mean retention time, i.e., the first moment of the retention probability density function (pdf) in the immobile domain, decides the second temporal moment of concentration. A mass transfer model with two first‐order rate coefficients can match up to the fourth temporal moment described by a multirate model with a predescribed pdf of the mass transfer rate coefficient. The kth temporal moment is finite when the (k‐1)th moment of the memory function exists.

Breakthrough curve tailing in a dipole flow field

Studying the tailing behavior of breakthrough curves (BTCs) is useful in the characterization of anomalous transport, matrix diffusion, and kinetic sorption. We analyze how BTCs of nonreactive and sorbing tracers behave at late time in well‐to‐well flow fields in homogeneous media. In the absence of regional flow, an asymptotic solution is derived for the traveltime distribution which follows a power law with exponent −4/3 at late times. With regional flow, the traveltime distribution exhibits a power law with exponent −4/3 over a certain period of time, followed by exponential decay. Dispersion influences the early time behavior but has little effect on the late‐time tailing. We also consider the BTC tailing of tracers undergoing kinetic sorption and diffusive mass transfer into immobile regions. If the memory function characterizing sorption kinetics is exponential, the late‐time behavior of the BTC is controlled by the traveltime distribution and thus follows a power law with exponent −4/3. In case of a matrix diffusion model, the memory function exhibits a power law with exponent −1/2, and the BTC in the dipole flow field follows a power law with exponent −7/6 in an intermediate time range, which differs from the exponent of −3/2 observed in uniform flow. Our analysis demonstrates that the flow configuration has to be considered when the tailing behavior of BTCs is used to characterize mass transfer kinetics. In particular, truncating a well‐to‐well tracer test at times where the traveltime distribution still follows the power law behavior may lead to the erroneous interpretation that the power law tailing of the BTC is caused by matrix diffusion.

Modeling Nonequilibrium Solute Transport in Heterogeneous Soils with Considerations of Mass-Transfer Processes and the Effects of Vadose Zone Properties

Heterogeneous unsaturated soil layers comprise both mobile and immobile regions as characterized by different gas-flow velocities. The movement of pollutants is governed by advection and dispersion...

Channel flow and trichloroethylene treatment in a partly iron-filled fracture: Experimental and model results

Technical developments have now made it possible to emplace granular zero-valent iron (Fe 0) in fractured media to create a Fe 0 fracture reactive barrier (Fe 0 FRB) for the treatment of contaminated groundwater. To evaluate this concept, we conducted a laboratory experiment in which trichloroethylene (TCE) contaminated water was flushed through a single uniform fracture created between two sandstone blocks. This fracture was partly filled with what was intended to be a uniform thickness of iron. Partial treatment of TCE by iron demonstrated that the concept of a Fe 0 FRB is practical, but was less than anticipated for an iron layer of uniform thickness. When the experiment was disassembled, evidence of discrete channelised flow was noted and attributed to imperfect placement of the iron. To evaluate the effect of the channel flow, an explicit Channel Model was developed that simplifies this complex flow regime into a conceptualised set of uniform and parallel channels. The mathematical representation of this conceptualisation directly accounts for (i) flow channels and immobile fluid arising from the non-uniform iron placement, (ii) mass transfer from the open fracture to iron and immobile fluid regions, and (iii) degradation in the iron regions. A favourable comparison between laboratory data and the results from the developed mathematical model suggests that the model is capable of representing TCE degradation in fractures with non-uniform iron placement. In order to apply this Channel Model concept to a Fe 0 FRB system, a simplified, or implicit, Lumped Channel Model was developed where the physical and chemical processes in the iron layer and immobile fluid regions are captured by a first-order lumped rate parameter. The performance of this Lumped Channel Model was compared to laboratory data, and benchmarked against the Channel Model. The advantages of the Lumped Channel Model are that the degradation of TCE in the system is represented by a first-order parameter that can be used directly in readily available numerical simulators.

Multitracer Test Approach to Characterize Reactive Transport in Karst Aquifers

A method to estimate reactive transport parameters as well as geometric conduit parameters from a multitracer test in a karst aquifer is provided. For this purpose, a calibration strategy was developed applying the two-region nonequilibrium model CXTFIT. The ambiguity of the model calibration was reduced by first calibrating the model with respect to conservative tracer breakthrough and later transferring conservative transport parameters to the reactive model calibration. The reactive transport parameters were only allowed to be within a defined sensible range to get reasonable calibration values. This calibration strategy was applied to breakthrough curves obtained from a large-scale multitracer test, which was performed in a karst aquifer of the Swabian Alb, Germany. The multitracer test was conducted by the simultaneous injection of uranine, sulforhodamine G, and tinopal CBS-X. The model succeeds to represent the tracer breakthrough curves (TBCs) of uranine and sulforhodamine G and verifies that tracer-rock interactions preferably occur in the immobile fluid region, although the fraction of this region amounts to only 3.5% of the total water. However, the model failed to account for the long tailing observed in the TBC of tinopal CBS-X. Sensitivity analyses reveal that model results for the conservative tracer transport are most sensitive to average velocity and volume fraction of the mobile fluid region, while dispersion and mass transfer coefficients are least influential. Consequently, reactive tracer calibration allows the determination of sorption sites in the mobile and immobile fluid region at small retardation coefficients.

Influence of Pore-Water Velocity on Transport Behavior of Cadmium: Equilibrium versus Nonequilibrium

The effect of pore-water velocity (6–82 cm∕h) on transport behavior of cadmium was investigated in three soils using column experiments. The symmetrical bromide breakthrough curves indicated the absence of immobile water region at the applied pore-water velocities. The equilibrium model could not describe the breakthrough curves of cadmium, particularly at high pore-water velocities. The shorter residence times at higher pore-water velocities result in the more significant early breakthrough and long tailing, reflecting a higher degree of nonequilibrium. While both the two-site nonequilibrium model and the effective dispersion equilibrium model could describe the transport behavior of cadmium, the latter appeared to be inappropriate because it overestimated the dispersion coefficients as high as 6.3-fold compared with the coefficients obtained from the bromine breakthrough curves. Thus, the nonequilibrium model was used to analyze the results. With increasing pore-water velocity, the sorption rate coeffic...