Page 56 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

38 David A. Wood and Bin Yuan

For individual cylindrical shaped pores with water and oil two-phase
flow, the maximum retention concentration of fine particles onto rock
grains is expressed as Eq. (2.8) (Yuan and Moghanloo, 2016). This expres-
sion relates the increase of electric repulsive force to the low-salinity
water’s ability to decrease the maximum retention concentration.
" #
μ r 2 qf w 2
w FP 2πr
σ cr ðS w ; rÞ 5 1 2 ð Þ φS w 1 2 φ c (2.8)
2φS w r P F e y
Usually, the detachment/attachment of fines only leads to small
changes of permeability, although the straining/plugging of fines into
pore throats causes more significant formation damage. Hence, Yuan
et al. (2018a) incorporated the effects of fines straining only into the
damage of water-phase relative permeability. Based on the assumption of
the instant straining of those detached fines caused by low-salinity water,
the concentration of strained fines can be equal to the detached fines con-
centration (i.e., by subtracting the maximum retention concentration of
fine particles under different conditions of low-salinity water saturation
from the initially attached fines concentration). An implicit fractional flow
relationship considering fines migration and subsequent straining during
low-salinity waterflooding is expressed as Eq. (2.9):

f w S w ; x D Þ 5
ð
1 21

0
2 2
K ro μ 11β σ cr;initial 0; S wc Þ2 12 μ w r qf w 1 2 φ 12φ
FP
ð
w s 4πφr P F e y x D r c
B e C
11
K rw μ
B C
@ A
o
(2.9)
An iteration algorithm can calculate the fraction flow functions versus
water saturation at different locations, as shown in Fig. 2.8. At the loca-
tions near the injection well, the calculated fractional flow velocities
decline steeply, which means the decrease of water phase flowing veloci-
ties caused by the exaggerated fines migration close to the wellbores. In
addition, the flood-front water saturation can be obtained by the method
of Welge (1952) that increases due to the attenuation of fines migration as
the injected water moves further toward to the production well.
Fig. 2.9 indicates that with an increase of low-salinity water saturation
in the water-flooded reservoir, the average fluid salinity in reservoir