Adsorption Models and Contaminant Transport Modeling

Optical microscopic study of rock thin sections using dye tracers is a way to determine mineral-water contact (physical surface) areas if the water flows in rock matrix or fine fractures. The surface areas of particulate materials can be computed from particle size and geometry (cf. Sverdrup and Warfvinge 1993) or measured by BET gas adsorption methods. White and Peterson (1990) point out, however, that measured or computed surface areas of geological materials generally exceed their reactive surface areas. The reactive surface area (as de-hned by 5 ) is what we need to model sorption or reaction rates in porous media. 

What is the simplest adsorption model that can adequately define sorption in the system of interest for purposes of our study The simpler the model, the less information is needed to parameterize it. The distribution coefficient model requires only entry of the mass of sorbent in contact with a volume of water and a value for K,. Pesticide adsorption can often be modeled adequately using a simple K ) approach (cf. Lyman et al. 1982). For smectite and ver-miculite clays and zeolites that have dominantly pH-independent surface charge, ion-exchange or power-exchange models may accurately reproduce adsorption of the alkaline earths and alkali metals. If the system of interest experiences a wide range of pH and solution concentrations, and adsorption is of multivalent species by metal oxyhydroxides, then an electrostatic model may be most appropriate. 

A variety of adsorption models, from A, to the electrostatic adsorption models in MINTEQA2, have been coupled with hydrologic transport models. Available coupled codes and their attributes have been described and compared, in some detail, by Mangold and Tsang (1991) (see also Lichtner et al. 1996) and will not be considered here. 

The most commonly used adsorption model in contaminant transport calculations is the distribution coefficient, model. In large part this reflects the simplicity of including a value in transport calculations (cf. Freeze and Cherry 1979 Domenico and Schwartz 1990 Stumm 1992). Nevertheless, such applications should be limited to conditions where values can be expected to remain near constant during transport (cf. Reardon 1981). Alternatively, if a Kj can be confidently shown to be a maximal or minimal possible value, such calculations can provide bounding or conservative information on contaminant transport. The bounding minimum approach has become standard in the modeling radionuclide transport, for example (cf. Meijer 1992). 

System assumptions that should be valid for such applications include fluid flow in the porous media is isotropic and adsorption is fast, reversible, and linear (cf. Freeze and Cherry 1979). Given these constraints, the comparative transport of a conserved (nonadsorbed) tracer, such as Br , and an adsorbed or retarded species, such as Am, can be described as shown in Fig. 10.29. A comparison of migration distances of the two species after time t, is made at concentrations where C(measured)/Co(initial) = 0.5 for the conserved and adsorbed species. The migration distance X of the conserved species after time r is a measure of the average groundwater velocity (U), or X = vt. Similarly, the migration distance of the adsorbed species (X,) i related to its velocity of movement (v ) by Xf = vj. The retardation factor (/tj for the adsorbed species is then given by 

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