Page 256 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Inorganic Deposition 227

pressure, temperature, and ion strength. Many models are available to esti-
mate the activity coefficient of a particular species (Yuan and Todd,
1991), and the Pitzer theory is widely accepted for modeling ion-
interaction and implemented in software package (He et al., 1997, Pitzer,
1973, Kan and Tomson, 2012).
Mineral precipitation or dissolution rate can be modeled as follows
(Bethke, 2007):

Q β
r β 5 A β K β 1 2 (5.6)
K eq:β
2
where r β is the reaction rate, K β is the rate constant (mole/m s), A β is
2
3
the reactive surface area of mineral β (m /m of bulk volume of mineral),
K eq:β is the chemical equilibrium constant, and Q β is the activity product
for mineral β which can be determined using Eq. (5.7):
n aq
v k β
Q β 5 L a (5.7)
k
k51
is the stoichiometry coef-
where a β is the activity of component k and v k β
ficients. The rate constant K β for species β can be estimated using
Eq. (5.8):

E β 1 1
K β 5 k 0β exp 2 2 (5.8)
R T T 0
where k 0β is the reaction rate for reaction β at a reference temperature
T 0 , and it can be determined experimentally. E β is the activation of reac-
tion β.
For the purpose of illutration, we assume the reservoir pressure is
7000 psi, and temperature is 300 F, and at the wellhead, the pressure and

temperature are 14.7 psi and 80 F, respectively. Mixing Miller field for-

mation water samples with North Sea water using the composition shown
in Table 5.1, the scale index and concentrations of different minerals can
be calculated as shown in Fig. 5.6.

5.3.2 Dynamics of scale formation
In a supersaturated solution, both cations and anions are in constant
motion and move in and out of the influence scopes of other ions or
molecules. Ions with opposite electrically charges are attracted to form
clusters. The cluster is not a stable stage until it grows large enough to