Kinetic sorption models

The comparison of kinetic sorption models presented here was made possible by the use of the mixing-cell dynamic technique, which eliminates the masking effects of hydraulic dispersion. 

Nonlinear sorption of chem-bio agents can be based on the different kinetics of sorption. Chemical nonequilibrium must also be considered in real-world problems. One of the early kinetic sorption models used the CDE first-order reactions (Scott 2000). This is represented as follows ... 

Adsorption may also be modeled as a nonequilibrium process using nonequilibrium kinetic equations. In a kinetic model, the solute transport equation is linked to an appropriate equation to describe the rate that the solute is sorbed onto the solid surface and desorbed from the surface (Fetter, 1999). Depending on the nonequilibrium condition, the rate of sorption may he modeled using an irreversible first-order kinetic sorption model, a reversible linear kinetic sorption model, a reversible nonlinear kinetic sorption model, or a bilinear adsorption model (Fetter, 1999). 

The main goal of this chapter is to review the most widely used modeling techniques to analyze sorption/desorption data generated for environmental systems. Since the definition of sorption/desorption (i.e., a mass-transfer mechanism) process requires the determination of the rate at which equilibrium is approached, some important aspects of chemical kinetics and modeling of sorption/desorption mechanisms for solid phase systems are discussed. In addition, the background theory and experimental techniques for the different sorption/ desorption processes are considered. Estimations of transport parameters for organic pollutants from laboratory studies are also presented and evaluated. 

When extrapolated to a 1-meter barrier typical of field installations, predictions that incorporated kinetic sorption were essentially identical to those generated using an equilibrium model, due to the low hydraulic gradient and larger domain associated with field conditions. 

Transport models that assume reversible kinetic reactions for applied phosphorus Transport models that assume irreversible kinetic reactions for applied phosphorus Transport models that assume both reversible and irreversible reactions for applied phosphorus Nontransport sorption models that assume both reversible and irreversible kinetic reactions for applied phosphorus... 

Selim et al. (1976b) developed a simplified two-site model to simulate sorption-desorption of reactive solutes applied to soil undergoing steady water flow. The sorption sites were assumed to support either instantaneous (equilibrium sites) or slow (kinetic sites) first-order reactions. As pore-water velocity increased, the residence time of the solute decreased and less time was allowed for kinetic sorption sites to interact (Selim et al., 1976b). The sorption-desorption process was dominated by the equilib-... 

A number of kinetically based models have been used to study soil-pesticide reactions. In many cases, sorption of pesticides has been treated as a rapid-equilibrium, single-valued, reversible process. Some of these models are briefly outlined below. 

Between the simplicity of the model and the complexity of the TLM, there are several other sorption models. These include various forms of isotherm equations (e.g., Langmuir and Freundlich isotherms) and models that include kinetic effects. The generalized two-layer model (Dzombak and Morel, 1990) (also referred to as the DLM) recently has been used to model radionuclide sorption by several research groups (Langmuir, 1997a Jenne, 1998 Davis, 2001). Constants used in this model are dependent upon the concentration of background electrolytes and... 

Laboratory experiments, transport modeling, field data, and engineering cost analysis provide complementary information to be used in an assessment of the viability of an MNA approach for a site. Information from kinetic sorption/ desorption experiments, selective extraction experiments, reactive transport modeling, and historical case analyses of plumes at several UMTRA sites can be used to establish a framework for evaluation of MNA for uranium contamination (Brady et al, 1998, 2002 Bryan and Siegel, 1998 Jove-Colon et al, 2001). The results of a recent project conducted at the Hanford 100-N site provided information for evaluation of MNA for a °Sr plume that has reached the Columbia River (Kelley et al, 2002). The study included strontium sorption-desorption studies, strontium transport and hydrologic modeling of the near-river system, and evaluation of the comparative costs and predicted effectiveness of alternative remediation strategies. 

Laying aside, for the moment, all application problems, let us examine the inherent capabilities of kinetics. Reaction rates are the most obvious and most readily available output of these experiments. As with adsorption isotherms, empirical sorption or desorption data can simply be plotted as a function of time and the progress of the reaction can be visually examined. Such information as half-reaction time and time to establish a new equilibrium can be directly obtained from the plot. If, however, the objective of the research is to provide input for generalized sorption models, more quantita-live information will be necessary. 

Dzombak, D.A. and Morel, F.M.M., Sorption of cadmium on ferric oxide at high sorbate/sorbent ratios Equilibrium, kinetics, and modeling, J. Colloid Interf. Sci., 112, 588, 1986. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

The values for the exudation rate F, interaction coefficient (A), buffer power of exudate in soil b and the decomposition rate constant for the exudate k were adopted from Kirk (1999). The value of the forward rate constant was estimated from Scheckel and Sparks (2001), who evaluated kinetic adsorption data of Ni to different minerals where ranged from 2.5 x 10 to 9.78 X 10 s For the simulation, an average value of 5.00 x 10 was used. This value also coincides with the values that Kirk and Staunton (1989) suggested for the kinetic adsorption of Q to soil, where the values ranged from lO" to 10 2 s f This same value was assumed for the rate constant for the two-stage sorption model, a2- The fraction of type 1 sites (F ) was assumed to be 0.3. Table 7 summarizes all input parameter values. 

A new numerical solver RF-RTM for the reactive transport in fractured porous media was investigated. The simulator RF-RTM is a three-dimensional model, that can consider several nonequilibrium kinetic type models. This paper illustrates the accuracy with the finite element model for simulating decay reactions in fractured porous media. The presented results show the capability of RF-RTM to simulate transport of one or more species. The finite element model RF-RTM was verified for several situations when sorption occurs imder equilibrium conditions such as in Example 1 and 5, or in case of matrix diffusion such as in Example 4. Validation of the nonequilibrium model was shown in Example 3. The nonequilibrium model is verified only for homogenous media. Numerical modelling of the decay chain reactions in fractured porous media with a nonequilibrimn sorption model is treated for the first time. Especially the different penetrations of decay chain components in a fiacture-matrix system was illustrated through a series of simulations (see Example 6). Further research is needed to quantify the effect of nonlinear sorption in the migration of the contaminants with sequentially deca3ong processes in fractured porous media. 

Two model approaches are compared by simulating reactive transport of acenaphthene in a heterogeneous porous medium. In a Monte Carlo approach a Lagrangian onedimensional streamtube model is used to assess the transport behaviour at field scale for distances of up to 800 m. Aquifer properties are taken from results of field experiments characterising a test site in a shallow quaternary sand and gravel aquifer. The results of the streamtube model are compared to model results of a two-dimensional Eulerian model. Both models account for kinetic sorption, described as diffusive transport in intra-particle pores. 

Linearization of kinetic data. Jannasch and co-workers (17) have developed a very useful approach to identify the number of distinct processes that contribute to the observed overall kinetics and, hence, need to be considered in the development of a suitable kinetic model to evaluate the data. These authors have derived a linearized equation for kinetic sorption controlled by a number of separate processes. Their analysis assumes that only one process controls overall sorption at any time and that each process can be described by a first order reversible reaction ... 

Batch-experiments are well suited for the measurement of sorption kinetics on defined soil components such as oxides or clay minerals. For the transformation of kinetic data from these batch-experiments to transport processes in model soil columns attention has to be paid to the dependence of the kinetic sorption parameters on the concentration of the suspended particles. 

In the studies presented the model developed for sorption equilibrium [1] was extended also to sorption kinetics. Furthermore, an approximative procedure was outlined for the transformation of equilibrixim and kinetic sorption data from batch-experiments to transport processes in model soil columns. 

Continuing the derivation of the differential equation for sorption kinetics under model conditions, the combination of Eqs. (11), (13), and (2) yields... 

The dependence of the kinetic sorption parameters on the concentration of the adsorbent in the suspension of the batch-experiment is not negligible. Neglecting this concentration dependence for reversible sorption leads to wrong estimations of the transport velocity of the pollutant in sediment or soil. Therefore, environmentally relevant batch-experiments have to be made at adsorbent concentrations true to nature. If this is not possible, corrective calculations under the model conditions described could be performed as an approximation. 

---