Aqueous Species Card Options (-R)
Effective Diffusion Function Options
The diffusion coefficient is the proportionality factor in Fick's law that relates the diffusive transport flux to the gradient in solute concentration. Diffusion results in mass transport from regions of high solute concentration to regions of lower concentration and occurs as a result of the random thermal motion (Brownian motion) of molecules and atoms. In the constrained geometry of a porous medium, the effective diffusion coefficient is reduced compared to the diffusion coefficient in free aqueous solution. The functional relationship between the effective aqueous diffusion coefficient and the free-aqueous diffusion coefficient can be specified with one of the following options:
|
In a saturated porous medium, the cross-sectional area available for diffusion in the aqueous phase is reduced by the porosity. In unsaturated porous media there is an additional reduction in cross-sectional area available for diffusion as a result of the reduced volumetric water content. This the default option for ECKEChem. The default effective diffusion coefficient is 0. 
|
 |
||||||||||||||
|
The constant molecular diffusion option assumes that the effective diffusion coefficient in the porous media is equal to the free-water diffusion coefficient. For most simple aqueous species the free-water diffusion coefficient is about 10-5 cm2/s (10-9 m2/s). 
|
|||||||||||||||
|
This option uses the empirical formulation of Kemper et al., 1966. 
|
|||||||||||||||
|
This option follows the power function described in Campbell, 1985. 
|
|||||||||||||||
Activity Coefficient Model Options
The thermodynamic activities of aqueous solute species are usually defined on the basis of molalities. Thus, they can be described by the product of their molal concentrations and their molal activity coefficients. The activity coefficients are complex functions of the composition of the aqueous solution. In electrolyte solutions, the activity coefficients are influenced mainly by electrical interactions. Much of their behavior can be correlated in terms of the ionic strength, defined by:
Symbols | |
|---|---|
 |
ionic strength |
 |
molal concentration of species i |
 |
electrical charge of species i |
The three basic options for computing the activity coefficients of aqueous species in STOMP are models based respectively on the Davies equation, the B-dot equation of Helgeson , and Pitzer's equations. The Davies and B-dot equations, are only useful in dilute solutions up to ionic strengths of 1 molal. The Pitzer model is useful in highly concentrated as well as dilute solutions, but is limited in terms of the components that can be treated. A constant activity coefficient model is also available, where the activity coefficients for all species may be set to a constant value.
|
|
|||||||||||||||||
|
The Davies (1962) equation is normally only used for temperatures close to 25°C. It is only accurate up to ionic strengths of a few tenths molal in most solutions. 
|
|||||||||||||||||
|
The B-dot equation of Helgeson (1968) is parameterized from 0°C to 300°C for solutions of up to 3 molal ionic strength in which NaCl is the dominant solute. 
|
|||||||||||||||||
|
The Pitzer activity coefficient algorithm is based on a virial expansion (Pitzer, 1991), which reduces to a modified form of the Debye-Huckel formulation at low ionic strength. The virial expansion involves a sum over all possible binary and ternary short-range interaction terms.  The expansion coefficients Bij(I) and Cijk are determined through extensive experimental measurement over a range of pressure and temperature conditions.
|
|||||||||||||||||
References
Campbell, G.S. 1985. “Soil Physics with BASIC,” In Developments in Soil Science 14, Elsevier Science Publishers B.V., New York, New York.
Davies, C.W. 1962. Ion Association. London: Butterworths. pp. 37–53.
Helgeson, H. C. 1968. Evaluation of irreversible reactions in geochemical processes involving minerals and aqueous solutions I. Thermodynamic relations. Geochimica et Cosmochimica Acta, 32, 853877. New York, New York: Pergamon Press.
Kemper, W. D. and J.C. van Schaik. 1966. “Diffusion of salts in clay-water systems.” Soil Sci. Soc. Amer. Proc., 30:534-540.
Pitzer, K.S. (editor). 1991. Activity coefficients in electrolyte solutions (2nd ed.). C.R,C. Press. ISBN 0-8493-5415-3. Chapter 3. *Pitzer, K.S. Ion interaction approach: theory and data correlation, pp. 75–153.
ECKEChem Input Cards
- Conservation Equations Card
- Equilibrium Equations Card
- Equilibrium Reactions Card
- Gas Species Card
- Kinetic Equations Card
- Kinetic Reactions Card
- Lithology Card
- Solid Species Card
- Species Link Card
- Aqueous Species Card
- Exchanged Species Card
- Plot File Species Variables
- Reference Node Species Variables