Page 195 - Reservoir Formation Damage

Crystal Growth and Scale Formation in Porous Media 177

> 1 scale formation
= 1 equilibrium
(9-37)
< 1 scale dissolution

and k' c is a scale formation rate constant incorporating the above mentioned
shape factors and some constants. The minus sign in Eq. 9-35 is for the
reduction of porosity by scale formation at the pore surface. Thus,
assuming the rock porosity, (|) r, remains constant and substituting Eq.
9-33 into 9-35 leads to an equation similar to Ortoleva et al. (1987):

rs (9-38)
dt
subject to

(9-39)

Assume that the surface area of crystal available for growth can be
expressed empirically by:

(9-40)

in which /(({>) is the specific surface of the mineral-fluid contact area
(surface area per unit mineral mass) expressed as a function of porosity.
Civan (1996) approximated this function according to Eq. 9-32. Thus,
substituting Eq. 9-40 into Eq. 9-23 leads to Holstad's (1995) equation:

(9-41)

Holstad (1995) expressed the temperature dependency of the crystal-
lization rate constant by the Arrhenius equation:

(9-42)
RT
where F M, A M, and E M denote an empirical mineral property factor, an
Arrhenius pre-factor, and the activation energy. Liu et al. (1997) used a
similar equation