Page 189 - Reservoir Formation Damage

Crystal Growth and Scale Formation in Porous Media 171

The minimum critical particle radius for a homogeneous nucleus to form
a stable deposit at a given super saturation state can be estimated by
equating the derivative of Eq. 9-17 to zero:

(9-18)
AG,,+£

Thus, the activation energy necessary for starting homogeneous nucleation
can be estimated by substituting Eq. 9-18 into Eq. 9-17 as:

AG =•
(9-19)

Crystallization Kinetics

The time necessary to initiate nucleation of crystals from a super-
saturated solution is called "induction time" (Reddy, 1995). It is a function
of the solution supersaturation, that is, the ratio of the ion activity product
to the solubility product of the precipitating crystalline matter as demon-
strated in Figure 9-4 by Reddy (1995) for calcium carbonate nucleation
in the presence of magnesium ions. Figure 9-4 indicates that the induction
time is lower for higher supersaturation. Below the supersaturation value
of about 10, the induction time for calcium carbonate nucleation is very
long. In this region, the solution is at a "metastable" condition and,
therefore, calcium carbonate crystals cannot be formed without the aid
of a matching growth surface or substrate (Reddy, 1995). It can also be
observed that the presence of magnesium ions increases the induction time
for calcium carbonate nucleation and therefore has a retardation and/or
inhibition effect. Reddy (1995) explains the magnesium ion inhibition of
calcium carbonate nucleation by adsorption of the magnesium ions and
thus, the occupation of some crystal growth sites on the calcium carbonate
crystal surface. For a quantitative interpretation of this phenomenon,
Reddy (1986; 1995) resorts to a growth rate analysis and a Langmuir
adsorption isotherm model using experimental data obtained by a seeded
growth method. He expressed the crystal growth rate as being proportional
to the surface available for crystal growth and the square of the driving
force for precipitation:

dN/dt = (9-20)

where N represents the calcium carbonate crystal concentration in the
solution in moles/liter, t denotes the time measured from the time of