Page 58 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

40 David A. Wood and Bin Yuan

decreases. As a result, the maximum retention concentration of fine
particles onto rock grains also decreases, which means that fine particles
are more likely to be dislodged as low-salinity waterflooding continues.
In addition, with an increase in low-salinity water saturation, the sensitiv-
ity of fines detachment to the changes of flowing velocity becomes more
significant. This phenomenon indicates that, in the late life of low-salinity
waterflooding, field operators need to be aware that any abrupt changes
of water injection and oil production rates can have significant impacts on
fines detachment.
For cases of low-salinity waterflooding with fines migration effects,
the mass-balance equation of fine particles and water flowing through the
porous media, taking into account the detachment and straining effects of
fine particles, can be expressed as Eq. (2.10) (pseudo-two-phase: water
(solids only exist in water phase)/oil; three-component: water/oil/fines):
8
@S wi @S wi
1 1
> @f wi @f wi
> 5 0
>
@S wi @x D
>
@t D @x D
< Swi
x D
! (2.10)
q @p
> k 0 k rw k ro
5 1
>
>
> μ μ
4πx D 1 1 βσ s w o @x D
:
The relationship expressed by equation 2.5x is a first-order, quasi-
linear, partial differential equation. The method of characteristics (MOC)
can be applied to solve this problem. For the equation 2.5x relationship,
the characteristic directions and the variations of water saturation along
the characteristic curves (lines) are expressed as Eq. (2.11):

dx D @f wi dS wi @f wi
5 ; 5 (2.11)
dt D @S w x D dt D @x D S w i
By combining the slopes of characteristic lines with the fraction flow
function (Eq. (2.9)), changes in water saturation can be computed. As
shown in Fig. 2.10, the effects of fines migration lead to the analytical
solutions of low-salinity waterflooding being significantly different from
conventional water flooding (i.e., with no changes of fluid salinity)
expressed as a classical Buckley-Leverett (1942) problem. In the conven-
tional waterflooding case, the characteristic velocity of the water-
saturation wave with a specific water-saturation value remains constant, as
it propagates toward the production well (i.e., the characteristic lines
remain straight, and along those lines water saturation remains constant).