Effective Retardation Factor Research Articles

Retardation factor scaling for contaminant transport in fractured media

This paper delves into the key factors governing contaminant retardation and the scaling of retardation factor for contaminant transport in naturally fractured media. It employs a geostatistical approach, utilizing hierarchical transition probability and covariance models, to characterize multimodal reactive mineral facies. Subsequently, scale-dependent models are developed to illustrate the transport behaviors of reactive contaminants under equilibrium sorption conditions and quantify the spatial and temporal variations of the effective retardation factor. These models incorporate various factors, including the structural characteristics of reactive minerals (the volume proportions and lengths of different facies types), fracture characteristics (the means and variances of fracture apertures), and the adsorption capacity of contaminants on minerals (sorption coefficients (ln Kd)). The results from these Lagrangian-based models are compared and validated against experimental data of solute transport in a single natural fracture. These findings underscore the remarkable agreement between the derived scale-dependent analytical expressions and the experimental results. Additionally, a global sensitivity analysis was performed using the Monte Carlo-based Sobol’ indices method to understand the influential factors governing contaminant retardation. The study reveals that the primary influential factor is the sorption capacity of contaminants on minerals, while fracture and reactive mineral structural characteristics play a secondary role. These insights provide significant information for understanding the reactive transport processes and the environmental impact of transport parameters in fractured media.

Assessment of membrane and diffusion behavior of soil-bentonite slurry trench wall backfill consisted of sand and Xanthan gum amended bentonite

The diffusion and semi-permeable membrane behavior are significant for evaluating pollution containment effectiveness of soil-bentonite slurry trench wall backfill (referred to as SB backfill) at contaminated sites. In this study, chemico-osmotic tests were performed on xanthan gum amended SB backfill (referred to as XGSB backfill) and conventional SB backfill utilizing zinc nitrate and lead nitrate solutions as tested liquids. The effective diffusion coefficient (D*), retardation factor (Rd), and chemico-osmotic efficiency coefficient (ω) of the backfills were evaluated. The results revealed that each tested backfill behaved as a semi-permeable membrane material with measured ω ranging from 0.015 to 0.14 and 0.007 to 0.05 when exposed to lead and zinc solutions with concentrations varying from 0.5 to 50 mM, respectively. The ω and Rd values for the backfills decreased with increasing concentrations of the tested solutions, while the D* of heavy metal cations increased, regardless of backfill type and tested solution type. Compared to the SB backfill, the ω and Rd of the XGSB backfill were higher while the D* was lower. The values of ω, D*, and Rd for the XGSB backfill were compared to those for soil-bentonite backfills in previous studies. A linear equation was presented to evaluate the correlation between ω and solute concentration in a semi-logarithmic scale. Finally, the advantages of considering membrane behavior in the design of slurry trench wall was discussed with the aid of an example analysis based on the measured ω and D* for the SB and XGSB backfill.

Assessment of Clay Mineral Attenuation Capacity for Human Viral Pathogens

The current practice of curbing the ill effects associated with the open dumping of biomedical waste (BMW) solely relies on incineration. However, the incineration of BMW and plastic-based medical gear is associated with severe health hazards due to toxic emissions. Many countries are resorting to incineration at unpermitted locations and open dumping due to the enormous surge in the generated BMW during the ongoing pandemic times. Such improper practice of incineration of BMW incineration and open dumping leads to significant environmental pollution. Therefore, an alternative and environmentally sustainable disposal facility is essential to avoid the negative effects of BMW disposal. In this study, the effectiveness of compacted clay-based barrier systems was explored, for the first time, for the encapsulation of virus-contaminated BMW. The model parameters essential for designing such exclusive BMW containment facilities, namely effective diffusion coefficient (De) and retardation factor (Rd) for different clay minerals, were evaluated. The evaluation was based on the limited available batch sorption test and free solution diffusion test data for various hazardous pathogens. The model parameters were utilized to understand the attenuation of viral pathogens (SARS-CoV, poliovirus, and reovirus) and bacteriophages (MS2 and φx-174) in montmorillonite and kaolinite mineral barriers. The selected pathogens were chosen such that they represented SARS-CoV-2 in terms of its surface characteristics. The results from the present study revealed that a 2- to 3- mm thick exclusive clay-based barrier system was sufficient to contain the studied pathogens and SARS-CoV-2 for 50 years.

Effects of local transverse dispersion on macro-scale coefficients of oxygen-limited biodegradation in a stratified formation

The correct characterization of macro-scale contaminant transport and transformation rates is an important issue for modeling reactive transport in heterogeneous aquifers. While previous studies have investigated field-scale heterogeneity of transport and biochemical properties, the effects of local transverse dispersion on macro-scale transport and transformation rates have not been well understood. In this paper, the process of oxygen-limited biodegradation in a stratified aquifer is analysed by spectral perturbation approach, and longitudinal macrodispersivity, effective biodegradation rate, effective retardation factor and effective velocity are derived for the coupled transport equations of a system consisting of a contaminant and an oxidizing agent (oxygen). The effects of local transverse dispersion on these macro-scale coefficients are studied. It is shown that local transverse dispersion can smooth the heterogeneity in biodegradation and sorption processes and enlarge effective biodegradation rate and retardation factor. The local transverse dispersion can also limit the effects of heterogeneity in biodegradation process on longitudinal macrodispersivities and effective velocities for the contaminant and dissolved oxygen. But the effects of heterogeneity in sorption process on the contaminant macrodispersivity is likely to be magnified by local transverse dispersion.

Analysis of Solute Transport from a Source with Finite Leachable Mass.

A general approach is developed for the analysis of solute transport from a source with a finite initial mass. The approach uses an effective retardation factor to assign the initial mass that can be leached from the source. Demonstration analyses are presented to illustrate the approach with the numerical simulator MT3DMS. For cases that are tractable with analytical solutions, comparisons between the numerical and analytical results confirm that the proposed approach yields correct results. The approach is straightforward to apply and can accommodate conditions ranging from pure advection to pure diffusion, effectively extending the capabilities of models to simulate sources with finite leachable masses for complex flow fields, reactions and distributions of sources.

Migration and sorption of strontium in clay-sand mixtures

The migration and sorption of Sr in clay-sand mixture were investigated by batch experiment, column experiments and numerical simulation. The results showed that as the clay content in clay-sand mixture increased, the effective porosity, absorption capacity and retardation factor of the mixture for Sr increased, but the dispersion coefficient and migration velocity decreased. The migration of Sr was influenced strongly when clay content was in range of 0–25 %, but influenced weakly when clay content was more than 25 %. The experimental data was consistent with the calculated results by CXTFIT program.

A Note on Upscaling Retardation Factor in Hierarchical Porous Media with Multimodal Reactive Mineral Facies

We present a model for upscaling the time-dependent effective retardation factor, \({\widetilde{R}}(t)\), in hierarchical porous media with multimodal reactive mineral facies. The model extends the approach by Deng et al. (Chemosphere 91(3):248–257, 2013) in which they expanded a Lagrangian-based stochastic theory presented by Rajaram (Adv Water Resour 20(4):217–230, 1997) in order to describe the scaling effect of \(\widetilde{R}(t)\). They used a first-order linear approximation in deriving their model to make the derivation tractable. Importantly, the linear approximation is known to be valid only to variances of 0.2. In this note, we show that the model can be derived with a higher-order approximation, which allows for representing variances from 0.2 to 1.0. We present the derivation and use the resulting model to recalculate \(\widetilde{R}(t)\) for the scenario examined by Deng et al. (2013).

Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian‐based transport model: 1. Time‐dependent effective retardation factor

AbstractThis series of papers addresses the transport of reactive solutes in groundwater. In part 1, the time‐dependent effective retardation factor, , of reactive solutes undergoing equilibrium sorption is linked to hierarchical stratal architecture using a Lagrangian‐based transport model. The model is based on hierarchical expressions of the spatial covariance of the log distribution coefficient, and the spatial cross covariance between and the log permeability, . The spatial correlation structure in these covariance expressions is the probability of transitioning across strata types of different scales, and they are parameterized by independent and quantifiable physical attributes of sedimentary architecture including univariate statistics for Y, , and the proportions and lengths of facies. Nothing is assumed about Y‐ point correlation; it is allowed to differ by facies type. The duration of the time‐dependent change in is a function of the effective ranges of the cross‐transition probability structures (i.e., the ranges of indicator correlation structures) for each scale of stratal architecture. The plume velocity and the effective retardation stabilize at a large‐time limit after the plume centroid has traveled a distance that encompasses the effective ranges of these cross‐transition probability structures. The well‐documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the model. The model gives a viable explanation for the observed PCE plume deceleration, and thus the observed can be explained by the process of linear equilibrium sorption and the heterogeneity in k and Kd. In part 2 [Soltanian et al., ], reactive plume dispersion, as quantified by the particle displacement variance is linked to stratal architecture using a Lagrangian‐based transport model.

A method for determining the extent of bulk 210Po and 210Pb adsorption and retardation in aquifers

The naturally-occurring radionuclides 210Po and 210Pb are normally found in very low concentrations in the environment. However, under some conditions 210Po contributes significantly to the radioactivity in ground waters and can constitute a health risk. Naturally-occurring 210Pb can be used in predicting the behavior of contaminant Pb. While studies have identified the processes controlling 210Po and 210Pb behavior, the extent of adsorption and rates of removal in an aquifer cannot be determined without quantifying the rates of supply of these isotopes from decay of parent nuclides on and within aquifer solids. This study demonstrates how the isotope systematics of the 238U decay series, which includes 210Po and 210Pb, can be used to quantify the adsorption and retardation factors of 210Po and 210Pb in aquifers. The rates of 210Po and 210Pb supply to ground waters are determined from the concentrations of other radionuclides in the series, especially 222Rn, and so the distribution coefficients between aquifer solids and groundwater can be calculated. The effects of different supply rates due to different distributions of parent radionuclides in the aquifer can then be separated from differences in adsorption, which is controlled by aquifer water chemistry. A review of groundwaters where 210Po, 210Pb, and 222Rn data are available indicates that systematic variations can be found in bulk effective adsorption coefficients and retardation factors. Overall, a method is provided for future studies of 210Po and 210Pb behavior, and greater understanding of the occurrence and migration of these radionuclides.

Natural Organic Matter Transport Modeling with a Continuous Time Random Walk Approach

In transport experiments through columns packed with naturally Fe/Al oxide-coated quartz sand, breakthrough curves (BTCs) of natural organic matter (NOM) displayed strong and persistent power law tailing that could not be described by the classical advection-dispersion equation. Tailing was not observed in BTCs for a nonreactive tracer (sulforhodamine B); therefore, the anomalous transport is attributed to diverse adsorptive behavior of the polydisperse NOM sample rather than to physical heterogeneity of the porous medium. NOM BTC tailing became more pronounced with decreases in pH and increases in ionic strength, conditions previously shown to be associated with enhanced preferential adsorption of intermediate to high molecular weight NOM components. Drawing from previous work on anomalous solute transport, we develop an approach to model NOM transport within the framework of a continuous time random walk (CTRW) and show that under all conditions examined, the CTRW model is able to capture tailing of NOM BTCs by accounting for differences in transport rates of NOM fractions through a distribution of effective retardation factors. These results demonstrate the importance of considering effects of adsorptive fractionation on NOM mobility, and illustrate the ability of the CTRW model to describe transport of a multicomponent solute.

Effective retardation factor for transport of reactive solutes in highly heterogeneous porous formations

[1] The effective retardation factor of highly heterogeneous porous formations is investigated using an analytical derivation and numerical simulations based on the self-consistent approximation and the multi-indicator conductivity model, used in the past for the effective hydraulic conductivity estimation. Both positive and negative correlation between the logarithm of hydraulic conductivity K and the logarithm of sorption distribution coefficient Kd are investigated, including the effects of random noise. The arithmetic average of the random retardation factor is found to represent accurately the effective retardation factor of isotropic and anisotropic formations regardless of correlation between ln Kd and ln K, and for variance of ln K as large as 8.

Vertical migration of leachate pollutants in clayey soils beneath an uncontrolled landfill at Huainan, China: A field and theoretical investigation

To assess the extent of leachate migration, continuous samples of clayey soils (about 9m) were obtained beneath a 17-year old uncontrolled landfill in southeastern China. The soil samples were sub sectioned and analyzed to determine the concentrations of chloride, sodium and COD in the pore water. Total nitrogen and soil organic matter content of the soil samples were also determined. Leachate-derived chloride was detected in the clayey soil to a maximum depth of 9m. Sodium and COD were found to migrate into the soils to depths of 3–4m due to the attenuation of solutes by the soil organic matter and clay minerals at the shallow soils. The estimated migration depths for the chloride are 3m in the case of pure diffusion. Advection and mechanical dispersion were found to be more important than molecular diffusion for this site with an 8m high leachate mound. By comparing the results obtained by the mathematical modeling for layered advection–dispersion problem with the measured concentration profiles, the ranges of the effective diffusion coefficient, retardation factor and dispersivity of the soils were estimated. Better fits are obtained by employing an artificial effective interface about 1m above the observed interface. The clayey soils showed a relatively high attenuation capacity for COD with the estimated retardation factor of 5.

Upscaling retardation factor in hierarchical porous media with multimodal reactive mineral facies

Aquifer heterogeneity controls spatial and temporal variability of reactive transport parameters and has significant impacts on subsurface modeling of flow, transport, and remediation. Upscaling (or homogenization) is a process to replace a heterogeneous domain with a homogeneous one such that both reproduce the same response. To make reliable and accurate predictions of reactive transport for contaminant in chemically and physically heterogeneous porous media, subsurface reactive transport modeling needs upscaled parameters such as effective retardation factor to perform field-scale simulations. This paper develops a conceptual model of multimodal reactive mineral facies for upscaling reactive transport parameters of hierarchical heterogeneous porous media. Based on the conceptual model, covariance of hydraulic conductivity, sorption coefficient, flow velocity, retardation factor, and cross-covariance between flow velocity and retardation factor are derived from geostatistical characterizations of a three-dimensional unbounded aquifer system. Subsequently, using a Lagrangian approach the scale-dependent analytical expressions are derived to describe the scaling effect of effective retardation factors in temporal and spatial domains. When time and space scales become sufficiently large, the effective retardation factors approximate their composite arithmetic mean. Correlation between the hydraulic conductivity and the sorption coefficient can significantly affect the values of the effective retardation factor in temporal and spatial domains. When the temporal and spatial scales are relatively small, scaling effect of the effective retardation factors is relatively large. This study provides a practical methodology to develop effective transport parameters for field-scale modeling at which remediation and risk assessment is actually conducted. It does not only bridge the gap between bench-scale measurements to field-scale modeling, but also provide new insights into the influence of hierarchical mineral distribution on effective retardation factor.

Robust solver based on modified particle swarm optimization for improved solution of diffusion transport through containment facilities

Accurate estimation of mass transport parameters is necessary for overall design and evaluation processes of the waste disposal facilities. The mass transport parameters, such as effective diffusion coefficient, retardation factor and diffusion accessible porosity, are estimated from observed diffusion data by inverse analysis. Recently, particle swarm optimization (PSO) algorithm has been used to develop inverse model for estimating these parameters that alleviated existing limitations in the inverse analysis. However, PSO solver yields different solutions in successive runs because of the stochastic nature of the algorithm and also because of the presence of multiple optimum solutions. Thus the estimated mean solution from independent runs is significantly different from the best solution. In this paper, two variants of the PSO algorithms are proposed to improve the performance of the inverse analysis. The proposed algorithms use perturbation equation for the gbest particle to gain information around gbest region on the search space and catfish particles in alternative iterations to improve exploration capabilities. Performance comparison of developed solvers on synthetic test data for two different diffusion problems reveals that one of the proposed solvers, CPPSO, significantly improves overall performance with improved best, worst and mean fitness values. The developed solver is further used to estimate transport parameters from 12 sets of experimentally observed diffusion data obtained from three diffusion problems and compared with published values from the literature. The proposed solver is quick, simple and robust on different diffusion problems.

Modeling Reactive Transport of Strontium‐90 in a Heterogeneous, Variably Saturated Subsurface

Sodium‐bearing waste (SBW) containing high concentration of 90Sr was accidentally released to the vadose zone at the Idaho Nuclear Technology and Engineering Center, Idaho National Laboratory, Idaho Falls, ID, in 1972. To investigate the transport and fate of the 90Sr through this 137‐m‐thick, heterogeneous, variably saturated subsurface, we conducted a two‐dimensional numerical modeling using TOUGHREACT under different assumed scenarios (low permeability of an entire interbed or just its surface) for the formation of perched water whose presence reflects the unique characteristics of the geologic materials and stratification at the study site. The results showed that different mechanisms could lead to different flow geometries. The assumption of low permeability for the entire interbed led to the largest saturated zone area and the longest water travel time (55 vs. 43 or 44 yr in other scenarios) from the SBW leakage to the groundwater table. Simulated water travel time from different locations on the land surface to the groundwater aquifer varied from <30 to >80 yr. The results also indicated that different mechanisms may lead to differences in the peak and travel time of a small mobile fraction of Sr. The effective distribution coefficient and retardation factor for Sr2+ would change more than an order of magnitude for the same material during the 200‐yr simulation period because of large changes in the concentrations of Sr2+ and competing ions. Understanding the migration rate of the mobile Sr2+ is necessary for designing long‐term monitoring programs to detect it.

Interpretation of the enhancement of field‐scale effective matrix diffusion coefficient in a single fracture using a semi‐analytical power series solution

AbstractA power series solution for convergent radial transport in a single fracture (PCRTSF) is developed. Transport processes considered in PCRTSF include advection and hydrodynamic dispersion in the fracture, molecular diffusion in the matrix, diffusive mass exchange across the fracture‐matrix interface, and mixing effects in the injection and the extraction boreholes. An analytical solution in terms of a power series in Laplace domain is developed first, which is then numerically inverted by de‐Hoog et al.'s algorithm. Four dimensionless parameters determine the behaviour of a breakthrough curve (BTC) calculated by PCRTSF, which are, in the order of decreasing sensitivity, the matrix diffusion factor, two mixing factors, and the Peclet number. The first parameter is lumped from matrix porosity, effective matrix diffusion coefficient, fracture aperture, and retardation factors. Its value increases as the matrix diffusion effect becomes significant. A non‐zero matrix diffusion factor results in a − 3/2 slope of the tail of a log–log BTC, a common property for tracer diffusion into an infinite matrix. Both mixing factors have equal effects on BTC characteristics. However, the Peclet number has virtually no effect on BTC tail. PCRTSF is applied to re‐analyse two published test results that were obtained from convergent radial tracer tests in a discrete, horizontal fracture in Silurian dolomite. PCRTSF is able to fit the field BTCs better than the original channel model does if a large matrix diffusion coefficient is used. Noticeably, the ratio of field‐scale to lab‐scale matrix diffusion coefficients can be as large as 378. This enhancement of the field‐scale matrix diffusion coefficient may be ascribed to the presence of a degraded zone at the fracture‐matrix interface because of karstic effects, or to flow channeling as a result of aperture heterogeneity. Copyright © 2009 John Wiley & Sons, Ltd.

Experimental and Numerical Investigations of Effects of Silica Colloids on Transport of Strontium in Saturated Sand Columns

Transport experiments with strontium were conducted using saturated sand columns in the presence and absence of silica colloids, and numerical modeling was performed with modeling results compared to experimental data. The experiments were aimed at testing the hypothesis that under certain chemical conditions colloids act as movement-retarding agents and yield a larger effective retardation factor for the migrating contaminant. Four individual experiments were conducted to identify conditions where the mobility of silica colloids is increased or decreased, and a similar set was conducted for strontium transport in the absence of colloids. Mobility of colloids was found to increase with decreasing ionic strength and increasing pH, with the ionic strength having the more significant impact. The reverse effect was obtained for strontium. Based on these results, two additional experiments were conducted where both colloids and strontium were injected at the column inlet. Results showed that under certain conditions of ionic strength and pH (I = 3.0 x 10(-2) M and pH = 4-5.4) colloids retarded the movement of strontium. The retardation effect was obtained in two experiments under slightly modified conditions, which confirms the role of colloids as retarding agents. Afinite difference numerical model was used to (a) simulate mobile breakthrough curves and compare to experimental data and (b) estimate the model parameters describing cotransport of strontium and colloids. The model accurately predicted arrival time and the overall shape of the breakthrough curves.

Numerical Modeling and Analysis of Solute Velocity and Macrodispersion for Linearly and Nonlinearly Sorbing Solutes in a Single Fracture with Matrix Diffusion

The behavior of the solute velocity and effective macrodispersivity of solute front in the fracture for the transport in a single fracture in the presence of rock matrix diffusion is analyzed using numerical modeling. The study is limited to a constant continuous solute source boundary condition in a single fracture with constant aperture. Analysis is made for linear and nonlinear sorption cases. Expressions are provided for solute velocity and effective macrodispersivity of the solute fronts during asymptotic and preasymptotic stages using spatial moment analyses. The effective retardation factor and dispersivity of solutes in the fracture are found to follow an exponential function with an exponent related to fracture-matrix parameters.

Temperature Effect on Migration of Zn and Cd Through Natural Clay

To investigate the effect of temperature on effective diffusion coefficients and retardation factors for Zn and Cd, combined diffusion and sequential extraction analyses were conducted at 15 degrees C and 55 degrees C. The effective diffusion coefficients of the metals increased up to ten times according to the increased temperature. On the other hand, the effect of temperature on the retardation factor depended on the retention mechanisms of the metals. The distribution coefficient for Zn, which was mainly partitioned in the carbonate phase, increased up to two times with the increase in temperature. On the other hand, the distribution coefficient for Cd, which was mainly partitioned in the exchangeable phase, was hardly affected by the temperature change. Results of combined diffusion and sequential extraction analysis showed that the effect of temperature on the heavy metals' (Zn and Cd) migration through the compacted natural clay was influenced by the combined effects of the diffusion coefficient and the retardation factor. Additionally, we could also observe the change in retention mechanism for the metals with the change in pore water concentration.

Stochastic analysis of transport and multicomponent competitive monovalent cation exchange in aquifers

Most stochastic analyses of reactive transport in physically and geochemically heterogeneous aquifers have focused on the analysis of a single reactive species. Here we conduct the stochastic analysis of multicomponent competitive monovalent cation exchange. Transport equations for dissolved cations are coupled with nonlinear cation exchange terms, which, for chemical equilibrium, are described by mass-action law expressions. These equations can be effectively decoupled by assuming that the weighted sum of cation concentrations is constant. The weight of each cation is equal to the reciprocal of its selectivity. Randomness of cation exchange capacity (CEC) leads to random retardation factors. Analytical expressions for effective retardation factors, longitudinal macrodispersivities, and concentration spatial moments are derived for a chemical system made of three monovalent cations (Na1 ,K 1 , and Cs 1 ) using the stochastic analytical solution of Miralles-Wilhelm and Gelhar (1996). Our results indicate that effective retardation factor, RC,i, spatial moments, and macrodispersivities of K1 are significantly different from those of Na1 . Effective retardation factors asymptotically attain their mean values after a transient phase of cationdependent duration. They strongly depend on the correlation between log-permeability (log K) and CEC. Pre-asymptotic effective retardation factor values for a negative correlation are smaller than the mean value, regardless of the value of the coefficient of variation of CEC (CVCEC). The smaller (larger) the variance of log K, , the great2 sf er (smaller) the effective retardation factor for a negative (positive) correlation. Cation