Ion exchange and adsorption are surface chemical or surface complexation processes leading to the exchange of chemical species between the aqueous solution and mineral surfaces present in geological porous formations (Jennings and Kirkner, 1984; Lichtner, 1985; Kharaka et al., 1988). Kharaka et al. (1988) explain the difference between ion exchange and adsorption as following: "The ion exchange model treats the exchange of cations or anions on a constant charge surface" and "the adsorption model simulates the exchange process on a surface where the surface charge is developed due to the ionization of surface sites at the solutionsurface interface." Therefore, adsorption is a more general concept and ion exchange is a special case of adsorption (Lichtner, 1985; Sahai and Sverjensky, 1998). Among the various surface complexation models, Sahai and Sverjensky (1998) facilitate the triple-layer model. Clays present in geological porous formations have many active ion exchange sites, a, occupied by various cations and cation exchange takes place for replacement of the cations in the order of the replacing tendency

The cation exchange capacity (CEC) of rocks can be expressed as the total number of moles of exchange sites a per unit mass of rock, Qaex, or per unit volume of rock, wa, which are related by (Lichtner, 1985):

Lichtner (1985) points out that "precipitation/dissolution reactions can alter the exchange capacity of the porous medium by creating or destroy

ing exchange sites," but this effect has not been taken into account in most reported studies. In Eq. 13-15, ɸ and Ps denote the porosity and the grain density of the rock, respectively. Represent the exchange sites by Na, the total number of different exchange sites by Na, an exchange site of type ot with unit charge by Ea, the i'h cation species with valence Zi by Si, and the concentration of the ith species attached to the exchange sites a by Cia, expressed in moles per unit bulk volume. Lichtner (1985) then describes the chemical reactions at mineral surfaces by

and the conservation of the ion exchange sites by

where N is the total number of chemically reacting species. Sj(Ea)zj and Si(Ea)zi represent the cations attached to the active exchange sites. Sears and Langmuir (1982) report that ion exchange and adsorption reactions in soils typically require a time of seconds to days to attain equilibrium. Therefore, Jennings and Kirkner (1984) describe these reactions by rate equations for full kinetic modeling. Applying their approach to Eq. 13-16 according to Chang and Civan (1997) yields the following kinetic expression for the rates of consumption of Sj (Ea )zj and production of Sf(Ea) zj respectively:

where ɸ is the porosity and Kirj and kirj denote the rate coefficients for the forward and reverse reactions, respectively. If Iaij" is the reaction rate for the exchange of the jth cation present in aqueous solution with the Ith cation attached to the ath site on the mineral surface, and Ir is the rate of the reactions of the /"'cation of the aqueous solution other than adsorption, the transport equation for the ithcation present in aqueous solution is given by (Lichtner, 1985):

where εa denotes the volume fraction of the aqueous phase in the bulk of porous formation and ci denotes the concentration of the ith cation in the aqueous solution, expressed in moles per unit volume of the aqueous phase. The balance of the ith cation adsorbed on the ath site of the mineral surface is given by (Litchner, 1985):

where Cia is the concentration of the ith species attached to the exchange sites a expressed in moles per unit bulk volume. Because

Thus, Lichtner (1985) combined Eqs. 13-19 and 20 into the following convenient form by summing Eq. 13-20 over all the exchange sites a, adding the resultant equation to Eq. 13-19, and eliminating the exchange reaction rates by means of Eq. 13-23:

Geochemical Modeling

As stated by Plummer (1992)*: "Geochemical modeling attempts to interpret and (or) predict chemical reactions of minerals, gases, and organic matter with aqueous solutions in real or hypothetical water-rock systems." Bassett and Melchior (1990) outlines the basic constituents and options of most geochemical models. Plummer (1992)* classified the various geochemical modeling efforts into four groups:

1. Aqueous speciation models for geochemical applications,

2. Inverse geochemical modeling techniques for interpreting observed hydrochemical data,

3. Forward geochemical modeling techniques for simulating the chemical evolution of water-rock systems, and

4. Reaction-transport modeling for the coupling of geochemical reaction modeling with equations describing the physics of fluid flow and solute transport processes.

Brief descriptions of these models are presented in the following, according to Plummer (1992).

Aqueous Speciation Models

Aqueous Speciation models describe the thermodynamic properties of aqueous solutions and they are an integral part of the geochemical models. Plummer (1992)* summarizes the constituents of these models as:

1. Mass balance equations for each element,

2. Mass action equations and their equilibrium constants, for complexion formation, and

3. Equations that define individual ion-activity coefficients.

Two types of aqueous specification models are popular:

(a) ionassociation models and

(b) specific interaction models.

The ion association and the specific interaction models facilitate, respectively, the extensions and a complex expansion of the Debye-Hiickel theory to estimate the individual ion activity coefficients of aqueous species (Plummer, 1992). The specific interaction models are preferred for highly concentrated solutions of mixed-electrolytes (Plummer, 1992). As pointed out by Plummer (1992), aqueous geochemical models can be used for forward and inverse geochemical modeling.


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