Page 157 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 135

during the salinity front propagation in area A. All suspended particles
that move into zone 4 are mobilized in A.
The salinity front enters the area B at the moment T mI . The attached
concentration ahead of the front is not zero; however, the maximum
retention function for high velocities U . U m is zero; thus, all attached
particles are removed by the salinity front. The particle release in zone B

corresponds to a vertical jump in the maximum retention curve at γ 5 γ I
to zero at γ 5 γ J (Fig. 3.20A). The suspended particles that move in zone
5 are those mobilized in A and released by the salinity front.
At the moment T mJ , the salinity front enters zone C. The particle
release in zone C corresponds to a jump in the maximum retention curve
at γ 5 γ I to some nonzero interval at γ 5 γ J . Some attached fines remain
behind the salinity front. The suspended particles that move in zones 6
and 7 are those mobilized in area B and released by the salinity front.
The salinity front enters the area D at the moment T crI . The attached
concentration ahead of the front is equal to S aI . The particle release in
zone D corresponds to a jump from horizontal line S aI to some nonzero-
interval of the curve γ 5 γ J . The suspended particles that move in zone 8
are those mobilized in area C and released by the salinity front.
At the moment T 1 , the salinity front by-passes zone 1. There are no
suspended particles ahead of the front. All the suspended particles that
move in zone 9 are those released by the salinity front.
Figs. 3.22B, C, and D show the evolution of the profiles for sus-
pended, strained and attached concentrations at different moments.
The profiles are taken at the above defined moments T 5 0, T mI , T 3 , T mJ ,
T crI , T 1 .

3.5.3.2 Injectivity decline prediction
The analytical model is now used to analyze well injectivity decline.
Typical values for the parameters drift delay factor α 5 0.05, filtration
coefficient λ 5 10 1/m, and formation damage coefficient β 5 1500 are
applied. A quadratic formula for the maximum retention function is used,
which corresponds to a model for mono-sized fine particles attached in
square pores, as derived in Bedrikovetsky et al. (2011a):
8
!
2
>
σ aI 1 2 ; U , U m γ ðÞ
< U
σ cr U; γð Þ 5 U m γðÞ ; (3.142)
>
0; U . U m γðÞ
: