Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.     

Transport modeling of copper and cadmium with linear and nonlinear retardation factors

The predictive accuracy of using the one-dimensional advection–dispersion equation to evaluate the fate and transport of solute in a soil column is usually dependent on the proper determination of chemical retardation factors. Typically, the distribution coefficient (K_d) obtained by fitting the linear sorption isotherm has been extensively used to consider general geochemical reactions on solute transport in a low-concentration range. However, the linear distribution coefficient cannot be adequately utilized to describe the solute fate at a higher concentration level. This study employed the nonlinear equilibrium-controlled sorption parameters to determine the retardation factor used in column leaching experiments. Copper and cadmium transportation in a lateritic silty-clay soil column was examined. Through the explicit finite-difference calculations with a third-order total-variation-diminishing (TVD) numerical solution scheme, all results of the theoretical copper and cadmium breakthrough curves (BTCs) simulated by using the Freundlich nonlinear retardation factors revealed good agreement with the experimental observations.     

Dissolution and sorption of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) and 2,4,6-trinitrotoluene (TNT) residues from detonated mineral surfaces

Composition B (Comp B) is a commonly used military formulation composed of the toxic explosive compounds 2,4,6-trinitrotoluene (TNT), and hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). Numerous studies of the temporal fate of explosive compounds in soils, surface water and laboratory batch reactors have been conducted. However, most of these investigations relied on the application of explosive compounds to the media via aqueous addition and thus these studies do not provide information on the real world loading of explosive residues during detonation events. To address this we investigated the dissolution and sorption of TNT and RDX from Comp B residues loaded to pure mineral phases through controlled detonation. Mineral phases included nontronite, vermiculite, biotite and Ottawa sand (quartz with minor calcite). High Performance Liquid Chromatography and Attenuated Total Reflectance Fourier Transform Infrared spectroscopy were used to investigate the dissolution and sorption of TNT and RDX residues loaded onto the mineral surfaces. Detonation resulted in heterogeneous loading of TNT and RDX onto the mineral surfaces. Explosive compound residues dissolved rapidly (within 9 h) in all samples but maximum concentrations for TNT and RDX were not consistent over time due to precipitation from solution, sorption onto mineral surfaces, and/or chemical reactions between explosive compounds and mineral surfaces. We provide a conceptual model of the physical and chemical processes governing the fate of explosive compound residues in soil minerals controlled by sorption-desorption processes.     

Comparison of nonideal sorption formulations in modeling the transport of phthalate esters through packed soil columns

Sorption of dimethyl phthalate (DMP), diethyl phthalate (DEP) and dipropyl phthalate (DPP) to two soil materials that vary in organic matter content was investigated using miscible displacement experiments under saturated flow conditions. Generated breakthrough curves (BTCs) were inversely simulated using linear, equilibrium sorption (LE), nonlinear, equilibrium sorption (NL), linear, first-order nonequilibrium sorption (LFO), linear, radial diffusion (LRD), and nonlinear, first-order nonequilibrium sorption (NFO) models. The Akaike information criterion was utilized to determine the preferred model. The LE model could not adequately describe phthalate ester (PE) BTCs in higher organic matter soil or for more hydrophobic PEs. The LFO and LRD models adequately described the BTCs but a slight improvement in curve-fitting was gained in some cases when the NFO model was used. However, none of the models could properly describe the desorptive tail of DPP for the high organic matter soil. Transport of DPP through this soil was adequately predicted when degradation or sorption hysteresis was considered. Using the optimized parameter values along with values reported by others it was shown that the organic carbon distribution coefficient (K(oc)) of PEs correlates well with the octanol/water partition coefficient (K(ow)). Also, a strong relationship was found between the first-order sorption rate coefficient normalized to injection pulse size and compound residence time. A similar trend of timescale dependence was found for the rate parameter in the radial diffusion model. Results also revealed that the fraction of instantaneous sorption sites is dependent on K(ow) and appears to decrease with the increase in the sorption rate parameter.     

Transport modes and pathways of the strongly sorbing pesticides glyphosate and pendimethalin through structured drained soils

Leaching of the strongly sorbing pesticides glyphosate and pendimethalin was evaluated in an 8-month field study focussing on preferential flow and particle-facilitated transport, both of which may enhance the leaching of such pesticides in structured soils. Glyphosate mainly sorbs to mineral sorption sites, while pendimethalin mainly sorbs to organic sorption sites. The two pesticides were applied in equal dosage to a structured, tile-drained soil, and the concentration of the pesticides was then measured in drainage water sampled flow-proportionally.The leaching pattern of glyphosate resembled that of pendimethalin, suggesting that the leaching potential of pesticides sorbed to either the inorganic or organic soil fractions is high in structured soils. Both glyphosate and pendimethalin leached from the root zone, with the average concentration in the drainage water being 3.5 and 2.7 μg L⁻¹, respectively. Particle-facilitated transport (particles >0.24 μm) accounted for only a small proportion of the observed leaching (13-16% for glyphosate and 16-31% for pendimethalin). Drain-connected macropores located above or in the vicinity of the drains facilitated very rapid transport of pesticide to the drains. That the concentration of glyphosate and pendimethalin in the drainage water remained high (>0.1 μg L⁻¹) for up to 7 d after a precipitation event indicates that macropores between the drains connected to underlying fractures were able to transport strongly sorbing pesticides in the dissolved phase. Lateral transport of dissolved pesticide via such discontinuities implies that strongly sorbing pesticides such as glyphosate and pendimethalin could potentially be present in high concentrations (>0.1 μg L⁻¹) in both water originating from the drainage system and the shallow groundwater located at the depth of the drainage system.     

Enhancement of chlorophenol sorption on soil by geophagous earthworms (Metaphire guillelmi)

Earthworms are the dominant soil biomass of many terrestrial ecosystems and markedly influence the physico-chemical and biological properties of soil; however, little is known about the effects of earthworm activities on the environmental behavior of micropollutants in soil. We studied the sorption and desorption of 2,4-dichlorophenol, 2,4,6-trichlorophenol, and pentachlorophenol on geophagous earthworm (anecic Metaphire guillelmi) casts of various aging times and on the parent soil. The casts were characteristic of lower pH and higher content of fine particles (silt and clay) than the parent soil. The sorption of the chlorophenols on the soil and casts were well fitted to linear isotherms, with sorption capacity in the order of pentachlorophenol > 2,4-dichlorophenol > 2,4,6-trichlorophenol. The sorption on the cast with different aging time was quite similar and was higher than on the parent soil. The sorption on the soil did not change between pH 7.07 of the soil and pH 6.76 of the casts. The desorption hysteresis of the chlorophenols on the soil and casts was compound specific and 2,4,6-trichlorophenol showed the highest hysteresis. The higher sorption capacity of the casts was not owing to the lowered pH of the casts, but mainly to the higher fine particles in the casts and the possible changes of nature of the soil organic matter through the earthworm gut passage. Our results indicate that geophagous earthworms may change sorption behavior and thus the bioavailability and transport of chlorophenols in soil. Earthworm effects should be considered when evaluating the environmental behavior and risk of organic pollutants in the ecosystems where earthworms are abundant.     

Effects of chemical oxidation on sorption and desorption of PAHs in typical Chinese soils

In situ chemical oxidation is a commonly applied soil and groundwater remediation technology, but can have significant effects on soil properties, which in turn might affect fate and transport of organic contaminants. In this study, it was found that oxidation treatment resulted mainly in breakdown of soil organic matter (SOM) components. Sorption of naphthalene and phenanthrene to the original soils and the KMnO₄-treated soils was linear, indicating that hydrophobic partitioning to SOM was the predominant mechanism for sorption. Desorption from the original and treated soils was highly resistant, and was well modeled with a biphasic desorption model. Desorption of residual naphthalene after treating naphthalene-contaminated soils with different doses of KMnO₄ also followed the biphasic desorption model very well. It appears that neither changes of soil properties caused by chemical oxidation nor direct chemical oxidation of contaminated soils had a noticeable effect on the nature of PAH-SOM interactions.     

Sorption of humic substances on aquifer material at artificial recharge of groundwater

Experiments in batch equilibrium system were carried out to evaluate the importance of physical and chemical factors determining the sorption efficiency of humic substances (HS) on aquifer material, which has been used for artificial recharge of groundwater (ARG) in drinking water production. Results showed that an increase of the amount of clay in the aquifer material and a decrease of pH in water increased the sorption efficiency. The sorption of higher molecular weight, more hydrophobic and aromatic HS (Aldrich and forest soil humic acids) were greater than the sorption of acidic HS (river fulvic acids), either on the aquifer material or to its representative sorbing phases, clay and organic matter. The sorption on the aquifer material was largely due to physical sorption (hydrophobic attractions). This study showed the importance of HS composition on their removal during ARG and contributed to an understanding of the HS sorption mechanisms in this process.     

Experimental determination of sorption in fractured flow systems

Fracture "skins" are alteration zones on fracture surfaces created by a variety of biological, chemical, and physical processes. Skins increase surface area, where sorption occurs, compared to the unaltered rock matrix. This study examines the sorption of organic solutes on altered fracture surfaces in an experimental fracture-flow apparatus. Fracture skins containing abundant metal oxides, clays, and organic material from the Breathitt Formation (Kentucky, USA) were collected in a manner such that skin surface integrity was maintained. The samples were reassembled in the lab in a flow-through apparatus that simulated approximately 2.7 m of a linear fracture "conduit." A dual-tracer injection scheme was utilized with the sorbing or reactive tracer compared to a non-reactive tracer (chloride) injected simultaneously. Sorption was assessed from the ratio of the first temporal moments of the breakthrough curves and from the loss of reactive tracer mass and evaluated as a function of flow velocity and solute type. The breakthrough curves suggest dual-flow regimes in the fracture with both sorbing and non-sorbing flow fields. Significant sorption occurs for the reactive components, and sorption increased with decreasing flow rate and decreasing compound solubility. Based on moment analysis, however, there was little retardation of the center of solute mass. These data suggest that non-equilibrium sorption processes dominate and that slow desorption and boundary layer diffusion cause extensive tailing in the breakthrough curves.     

Sorption of heterocyclic compounds from a complex mixture of coal-tar compounds on natural clayey till

The sorption and desorption of heterocyclic organic compounds in a complex multisolute system to a natural clayey till was investigated. The composition of the solutes reflect a simplified composition of an aqueous phase in contact with coal tar. Sorption was studied for two ratios (s:l) of clayey till (solid) to aqueous phase (liquid). The effect of the complex mixture of solutes on sorption of the four heterocyclic compounds: benzofuran, dibenzofuran, benzothiophene, and dibenzothiophene is evaluated by comparison with their sorption measured in single-solute systems. Sorption of the four compounds is affected by the complex mixture, with sorption decreases for all four compounds at high s:l ratio indicating competitive sorption. The effect on sorption of the individual compounds is not related to solubility or hydrophobicity of the compounds. Freundlich-type isotherms are observed for all compounds in the high s:l-ratio experiments, but for the most hydrophobic compounds isotherms are close to linear. The sorption of N-compounds and benzofuran is apparently influenced by cation exchange and dipole–dipole attraction to clay minerals. At high concentrations a dramatic increase in the sorption of the most strongly sorbing compounds is observed in the low s:l-ratio experiment. The dramatic increase in sorption appears to be a result of multimolecular layer sorption or condensation on surfaces in the clayey till at high surface density of organic compounds, and the data are fitted by BET (Brunauer, Emmet, and Teller) type 2 isotherms. The increase may or may not be induced by the presence of N-heterocyclic compounds sorbed by cation exchange and dipole–dipole attraction. The desorption of the compounds was studied for the low s:l ratio where multimolecular layer formation apparently had occurred. Partially irreversible sorption, hysteric Langmuir type desorption with isotherms of very high K_l coefficient, or behaviour reflecting dissolution of a condensed phase is observed.     

Modeling colloid-facilitated transport of multi-species contaminants in unsaturated porous media

Colloid-facilitated transport has been recognized as a potentially important and overlooked contaminant transport process. In particular, it has been observed that conventional two phase sorption models are often unable to explain transport of highly sorbing compounds in the subsurface appropriately in the presence of colloids. In this study a one-dimensional model for colloid-facilitated transport of chemicals in unsaturated porous media is developed. The model has parts for simulating coupled flow, and colloid transport and dissolved and colloidal contaminant transport. Richards' equation is solved to model unsaturated flow, and the effect of colloid entrapment and release on porosity and hydraulic conductivity of the porous media is incorporated into the model. Both random sequential adsorption and Langmuir approaches have been implemented in the model in order to incorporate the effect of surface jamming. The concept of entrapment of colloids into the air-water interface is used for taking into account the effect of retardation caused due to existence of the air phase. A non-equilibrium sorption approach with options of linear and Langmuir sorption assumptions are implemented that can represent the competition and site saturation effects on sorption of multiple compounds both to the solid matrix and to the colloidal particles. Several demonstration calculations are performed and the conditions in which the non-equilibrium model can be approximated by an equilibrium model are also studied.     

Application of the method of temporal moments to interpret solute transport with sorption and degradation

In this note, we applied the temporal moment solutions of [Das and Kluitenberg, 1996. Soil Sci. Am. J. 60, 1724] for one-dimensional advective-dispersive solute transport with linear equilibrium sorption and first-order degradation for time pulse sources to analyse soil column experimental data. Unlike most other moment solutions, these solutions consider the interplay of degradation and sorption. This permits estimation of a first-order degradation rate constant using the zeroth moment of column breakthrough data, as well as estimation of the retardation factor or sorption distribution coefficient of a degrading solute using the first moment. The method of temporal moment (MOM) formulae was applied to analyse breakthrough data from a laboratory column study of atrazine, hexazinone and rhodamine WT transport in volcanic pumice sand, as well as experimental data from the literature. Transport and degradation parameters obtained using the MOM were compared to parameters obtained by fitting breakthrough data from an advective-dispersive transport model with equilibrium sorption and first-order degradation, using the nonlinear least-square curve-fitting program CXTFIT. The results derived from using the literature data were also compared with estimates reported in the literature using different equilibrium models. The good agreement suggests that the MOM could provide an additional useful means of parameter estimation for transport involving equilibrium sorption and first-order degradation. We found that the MOM fitted breakthrough curves with tailing better than curve fitting. However, the MOM analysis requires complete breakthrough curves and relatively frequent data collection to ensure the accuracy of the moments obtained from the breakthrough data.     

Calculating pesticide sorption coefficients (Kd) using selected soil properties

Pesticide soil/solution distribution coefficients ( Kd values), commonly referred to as pesticide soil sorption values, are utilized in computer and decision aid models to predict soil mobility of the compounds. The values are specific for a given chemical in a given soil sample, normally taken from surface soil, a selected soil horizon, or at a specific soil depth, and are normally related to selected soil properties. Pesticide databases provide Kd values for each chemical, but the values vary widely depending on the soil sample on which the chemicals were tested. We have correlated Kd values reported in the literature with the reported soil properties for an assortment of pesticides in an attempt to improve the accuracy of a Kd value for a specific chemical in a soil with known soil properties. Mathematical equations were developed from regression equations for the related properties. Soil properties that were correlated included organic matter content, clay mineral content, and/or soil pH, depending on the chemical properties of the pesticide. Pesticide families for which Kd equations were developed for 57 pesticides include the following: Carboxy acid, amino sulfonyl acid, hydroxy acid, weakly basic compounds and nonionizable amide/anilide, carbamate, dinitroaniline, organochlorine, organophosphate, and phenylurea compounds. Mean Kd values for 32 additional pesticides, many of which had Kd values that were correlated with specific soil properties but for which no significant Kd equations could be developed are also included.     

Part V—sorption of pharmaceuticals and personal care products

Background, aim, and scope  Pharmaceuticals and personal care products (PPCPs) including antibiotics, endocrine-disrupting chemicals, and veterinary pharmaceuticals are emerging pollutants, and their environmental risk was not emphasized until a decade ago. These compounds have been reported to cause adverse impacts on wildlife and human. However, compared to the studies on hydrophobic organic contaminants (HOCs) whose sorption characteristics is reviewed in Part IV of this review series, information on PPCPs is very limited. Thus, a summary of recent research progress on PPCP sorption in soils or sediments is necessary to clarify research requirements and directions. Main features  We reviewed the research progress on PPCP sorption in soils or sediments highlighting PPCP sorption different from that of HOCs. Special function of humic substances (HSs) on PPCP behavior is summarized according to several features of PPCP–soil or sediment interaction. In addition, we discussed the behavior of xenobiotic chemicals in a three-phase system (dissolved organic matter (DOM)–mineral–water). The complexity of three-phase systems was also discussed. Results  Nonideal sorption of PPCPs in soils or sediments is generally reported, and PPCP sorption behavior is relatively a more complicated process compared to HOC sorption, such as the contribution of inorganic fractions, fast degradation and metabolite sorption, and species-specific sorption mechanism. Thus, mechanistic studies are urgently needed for a better understanding of their environmental risk and for pollution control. Discussion  Recent research progress on nonideal sorption has not been incorporated into fate modeling of xenobiotic chemicals. A major reason is the complexity of the three-phase system. First of all, lack of knowledge in describing DOM fractionation after adsorption by mineral particles is one of the major restrictions for an accurate prediction of xenobiotic chemical behavior in the presence of DOM. Secondly, no explicit mathematical relationship between HS chemical–physical properties, and their sorption characteristics has been proposed. Last but not least, nonlinear interactions could exponentially increase the complexity and uncertainties of environmental fate models for xenobiotics. Discussion on proper simplification of fate modeling in the framework of nonlinear interactions is still unavailable. Conclusions  Although the methodologies and concepts for studying HOC environmental fate could be adopted for PPCP study, their differences should be highly understood. Prediction of PPCP environmental behavior needs to combine contributions from various fractions of soils or sediments and the sorption of their metabolites and different species. Recommendations and perspectives  More detailed studies on PPCP sorption in separated soil or sediment fractions are needed in order to propose a model predicting PPCP sorption in soils or sediments based on soil or sediment properties. The information on sorption of PPCP metabolites and species and the competition between them is still not enough to be incorporated into any predictive models.     

Formulation of a soil-pesticide transport model based on a compartmental approach

A semianalytical soil-pesticide transport model is formulated based on a compartmental approach to determine spatial and temporal variations of pesticide residues across a soil profile. The compartmental model is implemented by drawing an analogy between a series of continuous-flow stirred tank reactors and a soil horizon that consists of multiple perfectly mixed compartments. The analogy is strengthened by exploiting a relation between the compartment series and the conventional convective-dispersive equation (CDE) for vertical transport in the soil. Consequently, the number of compartments in the model formulation is not free, but dictated as a function of transport parameters. The model formulation allows consideration of arbitrary boundary value specifications and also, for some cases, spatially varying initial concentration profiles. Sorption kinetics is represented via a two-site model that involves a linear sorption isotherm and a first-order irreversible sorption or a radial diffusive penetrating model. For these three cases, analysis of the compartmental model allows the resultant concentration profiles to be expressed in terms of the Poisson distribution. When a nonlinear kinetic sorption model is used to simulate the sorption processes, an analytical solution is not found and a numerical approach is required.     

Effects of sorption on transverse mixing in transient flows

Transverse mixing has been identified as a potentially limiting factor for natural attenuation of plumes originating from continuously emitting sources. Under steady-state flow conditions, dispersion is the only process leading to lateral mixing. This process is very slow and cannot explain the lateral spread of plumes observed in the field. When the flow direction fluctuates with time, transverse dispersion is slightly enhanced, but not very pronounced. Under these flow conditions, however, sorption can contribute to mixing into the mean transverse direction. If the reacting compounds differ in their strength of sorption, chromatographic mixing and separation alternate in time-periodic flows. For instantaneous sorption, the plumes may overlap within a stripe of fixed width. In contrast to sorption in local equilibrium, kinetic sorption contributes to mixing also for compounds with identical sorption strength. I derive an analytical expression for the equivalent transverse dispersion coefficient of a kinetically sorbing compound in a spatially uniform flow field undergoing sinusoidal fluctuations in time. This expression may be used for reactive transport calculations in an equivalent domain with constant flow. The effects are the strongest for compounds with a dimensionless partitioning coefficient of about unity, slow sorption kinetics, and slowly fluctuating velocities. For realistic parameters, kinetic sorption contributes to transverse mixing in the same range as heterogeneity.     

Sorption isotherms of brominated diphenyl ethers on natural soils with different organic carbon fractions

Sorption isotherms of BDE-28 and BDE-47 on natural soils with different contents of soil organic matter (SOM) were investigated. Due to low water solubility of BDEs and resulted narrow ranges of aqueous equilibrium concentration, the linear distribution model showed similar and good fitting efficiency to the linear portion of nonlinear Freundlich curve. For the same sample, the linear and nonlinear model fitting sorption coefficients were close. At the statistically significant level of 0.05 or 0.1, significant relationships of total organic carbon fraction (fOC) with the fitting sorption coefficients can be observed. As for BDE-28, the relationships of fOC and SOM fractions with the single point partition coefficients at different aqueous concentrations of BDEs were significant; while for BDE-47, the relationships became less significant or insignificant, especially at higher aqueous concentrations. The findings in this study may facilitate more understanding on transport and fate of studied BDEs in soil systems.     

Sorption of naphthoic acids and quinoline compounds to estuarine sediment

The sorption of 16 ionizable organic compounds (IOCs) to an estuarine sediment was measured in synthetic estuarine water as a function of IOC concentration (1-100 microM) at fixed ionic strength (0.4 M), pH (7.6), and sediment concentration (0.018 g sediment kg(-1) suspension). Of the 16 IOCs, 11 were naphthoic acids and five were quinoline compounds. The linear sorption distribution coefficient (Kd) was used to correlate sorption to IOC physicochemical and molecular characteristics. With respect to naphthoic acid, sorption increased with the addition of ortho-substituent groups and with increasing chain length of the 1-acid group, and the greatest increase occurred with ortho-hydroxyl, carbonyl, and carboxyl groups. With respect to quinoline, sorption decreased with substituent group addition (except for nitro group) and with additional heterocyclic N atoms. For the naphthoic acids, log Kd exhibited a positive correlation with water solubility (log Sw) indicative of sorption primarily to mineral surfaces under the solution chemistry. For the quinoline compounds, log Kd exhibited a negative correlation with log Sw and a positive correlation with n-octanol/water partition coefficient (log K(OW)) indicative of sorption primarily to organic matter. For both compounds, poor or no correlations were established between log Kd and acid dissociation constant (pKa1), and between log Kd and a variety of molecular connectivity indexes. The results from this study demonstrate that the sorption of IOCs differ depending on their backbone structure and may differ between parent compound and ionizable degradation product.     

An analytically solved kinetic model for pesticide degradation in single compartment systems

An analytical kinetic model was developed to simulate the degradation of pesticides in systems such as soil or water. Based on a single compartment system, a set of simultaneous first-order differential equations was analytically solved by the eigenvalue and eigenvector method. The developed model is capable of simulating the concentrations of parent compound and any net of degradation products connected by irreversible reactions.