Page 191 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 165

ð X;ϕ 1 sX; ϕÞ
ð
T 5 dϕ 1 dX : (3.238)
ð
ð
0;0 fX; ϕÞ fX; ϕÞ
Fig. 3.28 presents the trajectories of saturation and concentration in
the (X, T)-plane.
An example calculation of the Impedance from Eq. (3.216) is given in
Fig. 3.29.
Relative phase permeability is given by Corey’s formulae:

n o
12s or 2s
k ro 5 k rowi
12s or 2s I
:
n w
(3.239)
s2s I
ð
k rw 5 k rwor = 1 1 βS s Þ
12s or 2s I
where the values of endpoint saturations and relative permeability are pre-
sented in Table 3.15 for injected and reservoir salinities.
The impedance initially rises when the injection fluid is high-salinity
water, but then declines gradually as more of the reservoir fills with the
less viscous injected water. When low-salinity water is used, fines detach-
ment causes the impedance to rise substantially.

3.7.6 Implementation of fines migration using reservoir
simulators
The explicit expressions for impedance derived here, i.e., those for well
productivity in Section 3.4 and well injectivity in Sections 3.5.3, 3.6.4,
and 3.7.3, can be implemented in 3D reservoir simulators.
The extent of formation damage zones during fines migration in pro-
duction and injection wells typically does not exceed 1 3m(Nunes
et al., 2010). Therefore, this damage can be accounted for in the skin fac-
tor. The main commercial 3D reservoir simulators contain well options,
where skin can be expressed by a table or formula, yielding the well
boundary condition for the damage-free flow in the reservoir. An exam-
ple of matching the analytical model for near-well formation damage
with the damage-free waterflooding is presented by Bedrikovetsky et al.
(2011c). Implementation of Shapiro’s model for menisci dynamics and
fines lifting by capillary forces is an important next development of fines
migration in two-phase flows (Shapiro 2015, 2016).