Page 349 - Reservoir Formation Damage

Inorganic Scaling and Geochemical Formation Damage 329

equilibrium assumption is usually considered reasonable (Walsh et al.,
1982, Lichtner, 1992; Liu et al., 1997; Liu and Ortaleva, 1996, 1996).
Consider an aqueous phase undergoing a total of Nf chemical aqueous
reactions, r = 1,2,...,Nf denotes the index for the various aqueous reactions.
represents the total number of aqueous species involved in the r th
N r
aqueous or homogeneous reaction. S a:a. = l,2,...,N r denotes the various
th
aqueous species involved in the r aqueous reaction. Then, the aqueous
reactions can be typically represented by (Walsh et al., 1982; Liu et al., 1996):

(13-3)

or simply as

(13-4)

where v/ a denotes the stochiometric coefficient of species a involved
in the r th aqueous reaction. Note v/ a is negative for the reactants and
positive for the products.
Applying the mass action law of Prigogine and DeFay (1954), the
chemical equilibria between the products and reactants of the r th reaction
can be expressed as (Walsh et al., 1982; Liu et al., 1996):

f ra f
N
r = 12
11 "a
K r =Y\a ' ' i,^,...,lV r (13-5)
a=l
K* denotes the thermodynamic equilibrium constant for the r th aqueous
reaction given as the ratio of the rate constants kjj and k, b of the forward
and backward reactions represented by Eq. 13-3:

(13-6)

is the chemical activity of the aqueous species a, which can be
fl a
expressed in terms of the molal concentration, C a, of species a as:

a (13-7)
~

in which y a is the activity coefficient determined by the Debye-Huckel
theory (Helgeson et al., 1970).