Retardation-factor models

Retardation-factor models, which incorporate a simple retardation factor derived from a linear- or linearized-distribution coefficient... 

There are various parameters and assumptions defining radionuclide behavior that are frequently part of model descriptions that require constraints. While these must generally be determined for each particular site, laboratory experiments must also be conducted to further define the range of possibilities and the operation of particular mechanisms. These include the reversibility of adsorption, the relative rates of radionuclide leaching, the rates of irreversible incorporation of sorbed nuclides, and the rates of precipitation when concentrations are above Th or U mineral solubility limits. A key issue is whether the recoil rates of radionuclides can be clearly related to the release rates of Rn the models are most useful for providing precise values for parameters such as retardation factors, and many values rely on a reliable value for the recoil fluxes, and this is always obtained from Rn groundwater activities. These values are only as well constrained as this assumption, which therefore must be bolstered by clearer evidence. 

Empirically determined retardation factors (either partition coefficients or breakthrough curve measurements, which are the change in solute concentration measured over time in laboratory or field experiments) have been widely used because of their inherent simplicity.162 Modeling of specific geochemical partition and transformation processes is not necessary if the retardation factor can be determined empirically. 

Fig. 32.3. Comparison of the simulation results from Figure 32.1 (solid lines), which were calculated using a surface complexation model, with a parallel simulation in which sorption is figured by the reaction Kd approach (dashed lines). In each case, the retardation factor Rf for Pb++ transport is two.

Adsorption has a significant impact on the movement of allelo-chemical substances in soil. Such movement in soil by water is important from the standpoint of mechanism of phytotoxin activity in the receiving species at a site remote from the donor plant. Adsorption reduces the solute concentration in the soil solution and consequently minimizes redistribution in the environment. Solute transport has been described by Pick s second law of diffusion and the kinetic models for adsorption and degradation of reactive solutes (, 44). The contribution of adsorption is measured and expressed as the retardation factor, R. 

In this discussion equation (8) is used to model the transport of TCE during the test. The parameters needed for the model include the effective dispersion/diffusion coefficients, retardation factor, and the pore fluid velocity. 

In summary while conceptually appealing, the application of complex multi-solute models for Sr sorption to zeolite is in the early stages of development. While preliminary results are encouraging, additional work is required to develop more efficient computational methods and develop an improved database for parameter estimation. The remainder of this section focuses on the simpler retardation factor approach. 

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

Using the Freundlich isotherm the shortfall of limitlessness is removed, moreover, as with the linear model, a transformation into a retardation factor Rf is possible. 

All chemical reactions comprise at least two species. For models of transport processes in groundwater or in the unsaturated zone reactions are frequently simplified by a basic sorption or desorption concept. Hereby, only one species is considered and its increase or decrease is calculated using a Ks or Kd value. The Kd value allows a transformation into a retardation factor that is introduced as a correction term into the general mass transport equation (chapter 1.1.4.2.3). 

A)jS, whether sampled from probability distribution functions or calculated by regression equations or surface-complexation models, can be used in many contaminant transport models. Alternate forms of the retardation factor equation that use a (Equation (3)) and are appropriate for porous media, fractured porous media, or discrete fractures have been used to calculate contaminant velocity and discharge (e.g., Erickson, 1983 Neretnieks and Rasmuson, 1984). An alternative approach couples chemical speciation calculations... 

Transport of radionuclides by colloids. Several numerical models have been developed to assess the potential magnitude of colloidal-facilitated transport of radionuclides compared to the transport of dissolved species. Vilks et al. (1998) proposed a simple modification to the standard equation for the retardation factor. The equation applies to the ideal case where colloids are not trapped by the rock matrix and the composition of the colloids and the rock matrix are the same ... 

The isotherms are incorporated into the transport models through the retardation factor R. The one-dimensional ADR equation for saturated media becomes... 

Applicability of the Isotherm or Retardation-factor-based Reactive Transport Models... 

Finally, the effects of retardation and sorption/desorption were included in the model. Kaolinite has a low CEC (about 0.01 mg/g) and low buffering capacity (Mitchell, 1993), hence retardation for ff+ transport may not be significant. However, due to the change in pH environment, the tortuosity and the presence of other species, there may be a significant influence of retardation to the transport of H+ (Acar and Alshawabkeh, 1993). An experimentally obtained retardation factor of Jid was applied to the rate of concentration change term for the mass transport equation of H+. 

A median value for the retardation factor was used (R=5.3) since BIOCHLOR accepts only one value for fliis parameter. The site was modeled using one anaerobic zone with one set of rate coefficients as shown in Table 23.1.12. This is justified because the dissolved ox-... 

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