Page 187 - Reservoir Formation Damage
P. 187
Crystal Growth and Scale Formation in Porous Media 169
Stumm and Morgan (1996) expressed the interface free energy change by
G :
^interface ~ A:w cw + A ~ ° sw) (9-5)
Thus Eq. 9-4 becomes:
AG = VAG + A cs(a c Ve (9-6)
where cw, cs, and sw denote the deposit-water, deposit-substrate, and
substrate-water interfaces, respectively. A denotes the surface area and o
denotes the interfacial free energy. G cs and o cw denote the surface
energies per unit surface area of the deposited particle-substrate interface
and the deposited particle-solution interface, respectively, e is the strain
energy per unit volume. V is the volume of particle formed by pre-
cipitation, o is the surface energy per unit particle surface. AG V is the
change of volume free energy from solution to solid phases per unit
particle volume, given by (Stumm and Morgan, 1996):
(9-7)
where k b is the Boltzmann constant, T is absolute temperature, v is the
molar volume, and a and a 0 are the activity of the mineral dissolved in
solution and its theoretical activity at saturation, respectively.
Considering a semi-spherical deposition of radius r over a planar
substrate surface as an approximation, such that (see Figure 9-3)
(9-8)
2U
(9-9)
A = (9-10)
By combining the various efforts, Eq. 9-6 can be expressed as (Walton,
1969; Putnis and McConnell, 1980; Richardson and McSween, 1989;
Schneider, 1997; and Stumm and Morgan, 1996):
