Page 193 - Reservoir Formation Damage

Crystal Growth and Scale Formation in Porous Media 175

for which the initial amount of crystals present per unit bulk medium is
given by

m c=m°, t = (9-24)

Relating the crystal shape to spherical shape, the mass and surface area
of the crystalline particle is given, respectively, by:

(9-25)

and

A = (9-26)

in which C { and C 2 are the shape factors, p c , is the density, and D c is
the diameter. k c is a crystallization rate constant. Thus, Eqs. 9-23 through
9-26 lead to the following model in which the shape factors and the
constant y 2 ) have been incorporated into the constant k' c:
(

(9-27a)

subject to

(9-27b)

where

> 1 crystal growth

= 1 equilibrium
(9-28)
< 1 crystal dissolution

For constant saturation, Eqs. 9-27a, b yield:

D - D, +kt (9-29)
For example, D c = 5 urn, and k = k' c(F s-l)/p c is equal to 1.4 and 10.3
um/s for calcium° carbonate crystal growth at 25 and 50°C, respectively,
using the Dawe and Zhang (1997) data.