The use of equilibrium expressions for sorption to natural particles in fate and transport models is often invalid due to slow kinetics. This paper reviews recent research into the causes of slow sorption and desorption rates at the intraparticle level and how this phenomenon relates to contaminant transport, bioavailability, and remediation. Sorption kinetics are complex and poorly predictable at present. Diffusion limitations appear to play a major role. Contending mechanisms include diffusion through natural organic matter matrices and diffusion through intraparticle nanopores. These mechanisms probably operate simultaneously, but the relative importance of each in a given system is indeterminate. Sorption shows anomalous behaviors that are presently not well explained by the simple diffusion models, including concentration dependence of the slow fraction, distributed rate constants, and kinetic hysteresis. Research is needed to determine whether adsorption/desorption bond energies may play a role alon...

Mechanisms of Slow Sorption of Organic Chemicals to Natural Particles

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The mobility and degradation of pesticides in soils and the pollution of groundwater resources

Mathematical models have become indispensable tools for studying vadose zone flow and transport processes. We reviewed the history of development, the main processes involved, and selected applications of HYDRUS and related models and software packages developed collaboratively by several groups in the United States, the Czech Republic, Israel, Belgium, and the Netherlands. Our main focus was on modeling tools developed jointly by the U.S. Salinity Laboratory of the USDA, Agricultural Research Service, and the University of California, Riverside. This collaboration during the past three decades has resulted in the development of a large number of numerical [e.g., SWMS_2D, HYDRUS-1D, HYDRUS-2D, HYDRUS (2D/3D), and HP1] as well as analytical (e.g., CXTFIT and STANMOD) computer tools for analyzing water flow and solute transport processes in soils and groundwater. The research also produced additional programs and databases (e.g., RETC, Rosetta, and UNSODA) for quantifying unsaturated soil hydraulic properties. All of the modeling tools, with the exception of HYDRUS-2D and HYDRUS (2D/3D), are in the public domain and can be downloaded freely from several websites.

Development and Applications of the HYDRUS and STANMOD Software Packages and Related Codes

The hydraulic conductivity function, which is required to solve the Richards equation, is difficult to measure. Therefore prediction methods are frequently used where the shape of the conductivity function is estimated from the more easily measured water retention characteristic. Errors in conductivity estimations can arise either from an invalidity of the prediction model for a given soil, or from an incorrect description of the retention data. This second error source is particularly important for soils with heterogeneous pore systems that cannot be adequately described by the usually used retention functions. To describe the retention characteristics of such soils, a flexible θ(ψ) function was formed by superimposing unimodal retention curves of the van Genuchten (1980) type. By combining this retention model with the conductivity prediction model of Mualem (1976), conductivity estimations for soils with heterogeneous pore systems are obtained. Estimated conductivities by this model and the classical van Genuchten-Mualem method can differ by orders of magnitude. Thus reported disagreements between measured and estimated conductivities may in some cases be due to an inadequate description of the retention data rather than due to a failure of the prediction model.

Hydraulic conductivity estimation for soils with heterogeneous pore structure

http://www.pc-progress.com/Documents/Jirka/Simunek_et_al_MacroFl_2002.pdf

Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone

Analytical solutions are presented for two convection-dispersion type transport models useful for studying simultaneous pesticide sorption and degradation. One solution is for the familiar two-site sorption model in which adsorption-desorption proceeds kinetically on one fraction of the sorption sites, and at equilibrium on the remaining sites. Another solution holds for two-region (or mobile-immobile liquid phase) transport appropriate for aggregated or fractured media (...)

Two-Site/Two-Region Models for Pesticide Transport and Degradation: Theoretical Development and Analytical Solutions

Dependence of pesticide degradation on sorption: nonequilibrium model and application to soil reactors

Quantitative laboratory study of pesticide sorption and degradation during transport can provide insight into the basic processes affecting pesticide fate in field soils. Accordingly, we demonstrate the application of analytical solutions of two-site/two-region transport models useful in studying simultaneous pesticide sorption and degradation. Soil-column displacement experiments involving H2O, Cl, and atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) were conducted during steady-state water flow at two pore-water velocities and two pesticide concentrations. The soil used is a Valois silry loam (coarse-loamy, mixed, mesic Typic Dystrochrept). Effluent data from these experiments were used to demonstrate the application of these analytical solutions, as well as a parameter-estimation computer program based on these solutions. The ability to use laboratory-derived estimates of equilibrium sorption parameters to describe sorption under flowing conditions was evaluated at each flow velocity. Significant correlation between soil sorption partitioning and degradation prevents the simultaneous determination of both processes using these solutions. However, estimates of degradation obtained from mass balances of the column data were useful in identifying the equilibrium sorption parameters. Data collected elsewhere for 2,4,5-T (2,4,5-trichlorophenoxyacetic acid) herbicide transport were used as an additional example of the application of the model with degradation. Strengths and weaknesses of the models, and suggestions for further study, are presented. A BREAKTHROUGH CURVES for SOlutCS leached through porous media have been observed for a variety of chemicals in a broad range of soils. Much of these data were obtained in laboratoryscale experiments and are reviewed elsewhere (Rao et al., 1979; van Genuchten and Wagenet, 1989; Brusseau and Rao, 1989a). Recently, Winters and Lee (1987) reported tailing of three trace organics during in situ experiments under field conditions. Similar observations have also been made for organic contaminant transport in groundwater systems (Goltz and Roberts, 1986). These results indicate a need for understanding the processes behind the tailing phenomenon as contaminant-transport models are being implemented in research and management. Several models have been proposed to describe asymmetric breakthrough curves where tailing is attributed to either chemical or physical nonequilibrium processes. One-site or two-site chemical-process models assume that sorption is not at equilibrium and has a time-dependent or kinetic component. On the other hand, physical-process two-region models assume that sorption is always at equilibrium, but that transfer to some sorption sites is diffusion controlled. A.P. Gamerdinger, Dep. of Soil Science, Univ. of Florida, Gainesville, FL 32611; R.J. Wagenet, Dep. of Soil, Crop, and Atmospheric Sciences, Cornell Univ., Ithaca, NY 14853; and M.Th. van Genuchten, USDA-ARS, U.S. Salinity Lab., 4500 Glenwood Drive, Riverside, CA 92501. Joint contribution from the Dep. of 891!, Crop, and Atmospheric Sciences, Cornell Univ., and the U.S. Salinity Lab. Received 29 June 1988. *Corresponding author. Published in Soil Sci. Soc. Am. J. 54:957-963 (1990). In these models, water is commonly divided into mobile and immobile regions. Brusseau and Rao (1989b) discussed intra-organic-matter diffusion as a third process that may contribute to the tailing of hydrophobic organic compounds. The desire to distinguish physical and chemical processes that result in asymmetric breakthrough curves has led experimentalists to use several solutes in soilcolumn studies. Tritiated water (H2O) is often used to determine if immobile water is present in the system (Rao et al., 1980; Nkedi-Kizza et al., 1983). This tracer is probably the most suited for measuring the macroscopic average pore-water velocity, v, and the dispersion coefficient, D. The Cl ion is also often used as a tracer, the advantage being that this tracer is safer to handle than radioactive tritium. However, the use of Cl is only effective in so far as this tracer truly behaves as a noninteracting solute, thereby mimicking the flow of water. If this is true, then it may be possible to define a retardation factor, R, of unity. Unfortunately, Cl often undergoes anion exclusion, especially in relatively fine-textured soils (Biggar and Nielsen, 1962; Corey et al., 1963; Jacobs, 1964), resulting in R < 1. Organic-chemical transport is simultaneously influenced by both sorption and degradation. Miscible-displacement techniques may be better suited to simultaneous study of sorption and degradation than are traditional batch techniques, as flowing conditions, even in the laboratory, may better represent dynamic, transient field conditions. Unfortunately, nonequilibrium sorption confounds the measurement of degradation in miscible-displacement studies. Likewise, chemically or biologically mediated transformations may complicate the measurement of sorption, particularly when sorption is time dependent. A survey of the literature reveals that, in most previous soil-column experiments, great efforts were taken to eliminate degradation during studies of sorption kinetics accomplished with pesticide-displacement experiments. Detailed study of asymmetric breakthrough curves may be accomplished through a combination of analytical solutions of candidate transport models and properly designed experiments. The theoretical development of the two-site sorption (equilibrium and kinetic) and two-region (mobile-immobile water) transport models under conditions in which the solute is being transformed has been presented by van Genuchten and Wagenet (1989). We presented a generic analytical solution that allows implementation of different hypotheses about the relative rates of degradation in the liquid and solid phases of a soil. Here, we show how the generic model can be used to advantage in the analysis of observed column effluent data for Cl, H2O, and atrazine, and for 2,4,5-T effluent data of van Genuchten (1974). We emphasize that the purpose of our study is not to provide a comprehensive analysis of atrazine movement, but rather to il-

Application of two-site/two-region models for studying simultaneous nonequilibrium transport and degradation of pesticides

Numerous studies have shown that a single sorption rate constant is insufficient to describe nonequilibrium sorption and transport of organic solutes in soil. To investigate the effect of sorption rate (or, more generally, sorption site) heterogeneity on solute transport, we proposed a model assuming a γ distribution for both sorption rate and partitioning coefficient (abbreviated as GS for gamma-distributed sites). The model was tested by a series of column leaching and batch sorption experiments conducted with atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) over various time scales. Observed asymmetry and a left-hand shift of measured breakthrough curves (BTCs) with increasing flow velocity (0.51 to 21.3 cm/h) or decreasing column length (15.5 to to 6.0 cm) were successfully predicted by GS with sorption parameters obtained from an independent experiment. However, two other distinct sorption site models, the two-site first-order sorption (TSFO) and the two-site spherical diffusion (TSSD), were not able to describe the observed BTCs unless parameter values were adjusted for each case. In batch sorption experiments, increasing equilibration time (ranging from 1 to 237 h) was found to generally increase the isotherm-derived partitioning coefficient (K D ). The increasing trend was independently well-predicted using the GS model with optimized parameters from the column studies. The TSSD was less successful and TSFO the least able to reconcile the entire range of change in K D . The weak time-scale dependency of GS found in both column and batch experiments supports the assumption that a wide range of heterogeneous sorption sites or domains have been involved in the overall sorption process but to a variable degree as time elapsed. Potential alteration of soil sorption properties by γ irradiation was also observed.

Description of Atrazine Transport in Soil with Heterogeneous Nonequilibrium Sorption

Many different processes influence chemical breakthrough patterns from soil columns, including chemical kinetics, diffusion, matrix geometry, and flow heterogeneity. TRANSMIT, a multiregion model that reflects many of these features, was used to simulate a suite of solute breakthrough curves from soil columns subjected to both transient and steady-state flow. When utilized as a two-region model, TRANSMIT matched analytical solutions for steady-state flow through two-region soils. The TRANSMIT model is easily expanded to describe a wide range of multiregion and two-dimensional geometries and is applicable to transient and steady-state flow typical of both laboratory experiments and field situations. Sorption and degradation parameters can be varied, and nonuniform surface boundary conditions, resulting from irrigation method and banded chemical placement, can be described.

Robert J. Wagenet

Papers

Two-Site/Two-Region Models for Pesticide Transport and Degradation: Theoretical Development and Analytical Solutions

Dependence of pesticide degradation on sorption: nonequilibrium model and application to soil reactors

Application of two-site/two-region models for studying simultaneous nonequilibrium transport and degradation of pesticides

Description of Atrazine Transport in Soil with Heterogeneous Nonequilibrium Sorption

A Multiregion Model Describing Water Flow and Solute Transport in Heterogeneous Soils