## K

% organic carbon

Sabljia132 presents very accurate equations for predicting the Koc of both polar and nonpolar organic molecules based on molecular topology, provided the organic matter percentage exceeds 0.1%. Karickhoff133 discusses in detail adsorption processes of organic pollutants in relation to Koc.

Winters and Lee134 describe a physically based model for adsorption kinetics for hydrophobic organic chemicals to and from suspended sediment and soil particles. The model requires determination of a single effective diffusivity parameter, which is predictable from compound solution diffusivity, the octanol-water partition coefficient, and the adsorbent organic content, density, and porosity.

Major problems are associated with using the linear distribution coefficient for describing adsorption-desorption reactions in groundwater systems. Some of these problems include the following135,136:

1. The coefficient actually measures multiple processes (reversible and irreversible adsorption, precipitation, and coprecipitation). Consequently, it is a purely empirical number with no theoretical basis on which to predict adsorption under differing environmental conditions or to give information on the types of bonding mechanisms involved.

2. The waste-reservoir system undergoes a dynamic chemical evolution in which changing environmental parameters may result in variations of Kd values by several orders of magnitude at different locations and at the same location at different times.

3. All methods used to measure the Kd value involve some disturbance of the solid material and consequently do not accurately reflect in situ conditions.

The Langmuir equation was originally developed to describe adsorption of gases on homogeneous surfaces and is commonly expressed as follows:

where Smax = maximum adsorption capacity (^g/g soil), k = Langmuir coefficient related to adsorption bonding energy (mL/g), S = amount adsorbed (^g/g solid), and C = concentration of adsorbed substance in solution (^g/mL).

A plot of C/S versus 1/C allows the coefficients k and Smax to be calculated. When kC << 1, adsorption will be linear, as represented by Equation 20.6.

The Langmuir model has been used to describe adsorption behavior of some organic compounds at near-surface conditions.137 However, three important assumptions must be made:

1. The energy of adsorption is the same for all sites and is independent of degree of surface coverage.

3. The maximum adsorption capacity (Smax) represents coverage of only a single layer of molecules.

In a study of adsorption of organic herbicides by montmorillonite, Bailey and colleagues138 found that none of the compounds conformed to the Langmuir adsorption equation. Of the 23 compounds tested, only a few did not conform well to the Freundlich equation.

The assumptions mentioned above for the Langmuir isotherm generally do not hold true in a complex heterogeneous medium such as soil. The deep-well environment is similarly complex and consequently the studies of adsorption in simulated deep-well conditions139 140 have followed the form of the Freundlich equation:

where S and C are as defined in Equation 20.6, and K and N are empirical coefficients.

Taking the logarithms of both sides of Equation 20.9:

Thus, log-log plots of S versus C provide an easy way to obtain the values for K (the intercept) and N (the slope of the line). The log-log plot can be used for graphic interpolation of adsorption at other concentrations, or, when values for K and N have been obtained, the amount of adsorption can be calculated from Equation 20.9. Figure 20.9 shows an example of adsorption isotherms for phenol adsorbed on Frio sandstone at two different temperatures. Note that when N = 1, Equation 20.9 simplifies to Equation 20.6 (i.e., adsorption is linear).

The Langmuir equation has a strong theoretical basis, whereas the Freundlich equation is an almost purely empirical formulation because the coefficient N has embedded in it a number of ther-modynamic parameters that cannot easily be measured independently.120 These two nonlinear isotherm equations have most of the same problems discussed earlier in relation to the distribution-coefficient equation. All parameters except adsorbent concentration C must be held constant when measuring Freundlich isotherms, and significant changes in environmental parameters, which would be expected at different times and locations in the deep-well environment, are very likely to result in large changes in the empirical constants.

An assumption implicit in most adsorption studies is that adsorption is fully reversible. In other words, once the empirical coefficients are measured for a particular substance, Equations 20.6 to 20.10 describe both adsorption and desorption isotherms. This assumption is not always true. Collins and Crocker140 observed apparently irreversible adsorption of phenol in flowthrough adsorption experiments involving phenol interacting on a Frio sandstone core under simulated deep-well Equilibrium concentration (mg/L)

FIGURE 20.9 Freundlich isotherm for phenol adsorbed on Frio Core. (From U.S. EPA, Assessing the Geo-chemical Fate of Deep-Well-Injected Hazardous Waste: A Reference Guide, EPA/625/6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.)

Equilibrium concentration (mg/L)

FIGURE 20.9 Freundlich isotherm for phenol adsorbed on Frio Core. (From U.S. EPA, Assessing the Geo-chemical Fate of Deep-Well-Injected Hazardous Waste: A Reference Guide, EPA/625/6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.)

temperatures and pressures. If adsorption-desorption is not fully reversible, it may be necessary to use separate Freundlich adsorption- and desorption-isotherm equations to model these processes in the deep-well environment.120

### Clay ion-exchange model

As noted above, adsorption isotherms are largely derived empirically and give no information on the types of adsorption that may be involved. Scrivner and colleagues39 have developed an adsorption model for montmorillonite clay that can predict the exchange of binary and ternary ions in solution (two and three ions in the chemical system). This model would be more relevant for modeling the behavior of heavy metals that actively participate in ion-exchange reactions than for organics, in which physical adsorption is more important.

The clay ion-exchange model assumes that the interactions of the various cations in any one clay type can be generalized and that the amount of exchange will be determined by the empirically determined cation-exchange capacity (CEC) of the clays in the injection zone. The aqueous-phase activity coefficients of the cations can be determined from a distribution-of-species code. The clay-phase activity coefficients are derived by assuming that the clay phase behaves as a regular solution and by applying conventional solution theory to the experimental equilibrium data in the literature.3

Scrivner and colleagues39 compared the ion-exchange model predictions with several sets of empirical data. The model predictions are very accurate for binary-exchange reactions involving the exchange of nickel ions for sodium and potassium ions on illite and less accurate for ternary reactions involving hydrogen, sodium, and ammonia ions. The deep-well environment, however, is very likely to have multiple exchangeable species (such as Na+, K+, Ca2+, and Mg2+), and injected wastes commonly have elevated concentrations of more than one heavy metal. These concentrations result in complex ion-exchange interactions that probably exceed the capabilities of the model.

### Triple-layer model

One of the more sophisticated models for describing adsorption phenomena in aqueous solutions is the triple-layer model (TLM), also called the Stanford General Model for Adsorption (SGMA) because it has been developed, refined, and tested over a number of years by faculty and researchers at Stanford University.141-143 The TLM separates the interface between the aqueous phase and the adsorbent surface into three layers: surface layer, inner diffuse layer, and outer diffuse layer. Each has an electrical potential, charge density, capacitance, and dielectric constant. Hydrogen ions are assumed to bind at the surface plane; electrolyte ions (such as Na+) bind at the inner diffuse plane. The surface is assumed to be coated with hydroxyl groups (OH), with each surface site associated with a single hydroxyl group. The hydroxyl-occupied surface sites may either react with other ions in solution or dissociate according to a series of reactions, with each having an associated equilibrium constant. Experimental terms relate the concentrations of the ions at their respective surface planes to those in the bulk solution. The sum of the charges of the three layers is assumed to be zero (i.e., the triple layer is electrically neutral). For all its sophistication, TLM is of limited value for predicting adsorption in deep-well environments120:

1. Site-binding constants have been determined for only a limited range of simple oxides with only one type of surface site. Multiple-surface site minerals occurring in the deep-well environment such as silicates, aluminosilicates, and complex oxides (such as manganese oxide) will require much more complex TLMs.

2. Fixed-charge minerals such as clay are even more complex than the multiple-surface site minerals, and both ion exchange and other types of adsorption must be measured to characterize absorption reactions fully.

3. Minerals with different adsorptive properties in the injection zone may interact to produce results different from those that would be obtained if each mineral were tested separately. No satisfactory model has been developed that predicts adsorption properties of mixtures based on the properties of individual adsorbents.

4. The TLM is based on laboratory measurements of adsorption on materials that are suspended in solution. No satisfactory methods for measuring and interpreting the adsorptive properties of intact host rock have been developed for TLM application.

5. The TLM has been developed using studies based on solutions of relatively low concentrations of dissolved compounds. The very saline and briny conditions found in the deep-well environment may require an entirely different model. 