Page 351 - Reservoir Formation Damage

Inorganic Scaling and Geochemical Formation Damage 331

a=l
(13-10)
and s = l,2,...,N. minerals

For a mineral s undergoing a dissolution/precipitation reaction r, the
reaction driving force is given by (Liu et al., 1996):

a=l
(13-11)
far

AG rs > 0 for mineral dissolution and AG ri < 0 for mineral precipitation. k rs
th th
denotes the dissolution rate constant of the r reaction of the s mineral.
Approximating the shape of the mineral grains by a sphere, and
assuming that the mineral reactions are kinetic reactions, Liu et al. (1996)
express the rate of dissolution or precipitation of the s th mineral by the
r th reaction by:

(13-12)

as being proportional to the number of the s th mineral grains per forma-
2
tion bulk volume, n s, the surface area of the s th mineral grain, 47i/?^ ,
and the reaction driving force, AG rj. The grain mass density of the s th
mineral, p 5 , is inserted to express the mass rate of dissolution or pre-
cipitation of the i th mineral grain. R s represents the radius of the s th
mineral grain. Thus, Liu et al. (1996) express the rate of change of the s th
grain radius by dissolution and/or precipitation by various reactions as:

(13-13)
3r r=l

The mass conservation equation for species a undergoing transport
through porous media by various mechanisms is given by Eq. 7-34
derived in Chapter 7. The rate of generation of the Oi th aqueous species
per bulk formation volume, required for Eq. 7-34, is given by Liu et al.
(1996) as:
s
N r
wf
N
2
+a
W
/ vv YY r s ~ ia.-* " ^^•••i^a (13-14)
J
-a = l
l
r=l r=\