Page 183 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

158 Thomas Russell et al.

where the fractional flow function f is:

k rw ðs;γ;σ s Þ
f ðs; γ; σ s Þ 5 μ w : (3.202)
k rw ðs;γ;σ s Þ k ro ðs;γÞ
1
μ w μ o
The effect of fines straining on the aqueous phase flow is expressed as
(Coronado and Dı ´az-Viera, 2017; Zeinijahromi et al., 2013):
ð
k rw s; γÞ
k rw s; γ; σ s Þ 5 : (3.203)
ð
1 1 βσ s
Eq. (3.204) provides the mass conservation law for the salt, which is
assumed to only exist within the aqueous phase. Here, both the capillary
effects and advective dispersion are ignored (Omekeh et al., 2013):

ð
φ @ðγsÞ 1 1 @ rγfUÞ 5 0: (3.204)
@t r @r
In an oil-water system, a portion of the surface area of the porous
space is occupied by water, and the remainder by oil. It is assumed that
fines detachment is only possible where the rock surface is coated by
water, as the salt transfer that governs the electrostatic force (Section 3.2)
occurs only in the aqueous phase.
The overall attached fine particle concentration can be expressed as
the total of the particles attached to the water-accessible surface and those
attached to the oil-accessible surfaces.
Fines detachment here is modeled without a delay in detachment.
Thus, the attached concentration is given by (Borazjani et al., 2017;
Mohammadmoradi et al., 2017):

ð
ð
A w s; θÞ A 2 A w s; θÞ
σ a 5 σ cr γðÞ 1 σ aI ; (3.205)
A A
where A w is the area of the pore surface covered by water and A is the
total pore surface area.
The conservation law for suspended, attached, and strained fines, simi-
larly ignoring capillary effects and advective dispersion, is:
@ 1 @
ð φsc 1 σ a 1 σ s Þ 1 ð rcfUÞ 5 0: (3.206)
@t r @r