Page 224 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

198 Bin Yuan and Rouzbeh G. Moghanloo

The formation damage caused by both attached and strained fines is
incorporated into the retardation term in the relative permeability of the
water phase. Hence, the fractional flow function can be updated as:

21
k ro μ 11φβ S s 1φβ S a Þ
ð
w
s
a
f w S w ; S s ; S a Þ 5 11 (4.17e)
ð
k rw μ o
The existence of nanoparticles helps control fines migration by
increasing the maximum (critical) retention concentration of fine particles
onto rock grains, as shown in Eq. (4.17f):
2
2 0 1 3
μr 2 q
6 B FP 2πr C 7
σ cr x D ;C NP Þ5 12 B C 7 φ
ð
6
h
4 @ i A 5
2φr P y F ei1 128πr FP n N k B T 2κh 11K NP C NP ðς GS2ς NP Þς FP
K NP C NP
e
κ
(4.17f)
Here, introduce the following dimensionless variables for simplifica-
tion, as shown in Eq. (4.17g):
2
r qt σ a σ s 4k 0 π
x D 5 ; t D 5 ; Λ a 5 r e λ a ;Λ s 5 r e λ s ;S a 5 ;S s 5 ;P 5 p
2 φ φ
r e φπr e q
(4.17g)
The initial conditions of both attached and suspended fines are summa-
rized in Fig. 4.11. According to the assumptions of the maximum retention-
concentration model (Bedrikovetsky et al., 2011), the release of the initial
attached fines occurs instantly in conditions above the maximum limits.
As shown in Fig. 4.11A, around the well vicinity, all the initially attached
fines are released instantly because of the high flowing velocity. Within the
range of medium flow velocities, the concentration of released fines equates
to the difference between the initial attached fines concentration and the
maximum fines retention concentration, depending on flow velocity at that
location. In remote areas from the wellbore, there are no fines to be released
because of sufficiently slow fluid velocities. In Fig. 4.11B, the adsorption
of nanoparticles can enhance the attachment of fines effectively, i.e., no fines
are released within the range of nanoparticles treatment. Even for the injec-
tion of new fines, within the nanofluid treatment range, the rock grains can
have sufficient remaining capacity to capture those introduced fine particles,
until the maximum fines retention concentration with nanoparticles effects
is reached, which typically occurs after a sufficiently long-time interval.