Page 156 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

134 Thomas Russell et al.

Solving in zone 2, the parameter along the characteristic lines is X.
The suspended concentration is equal to zero (row 17 in Table 3.8).
Strained concentration in all zones is obtained from Eq. (3.121) by
integration of suspended concentration in time.
Dimensionless pressure drop across the core is calculated from Darcy’s
law (Eq. (3.124)):

1 ð 1 1 1 βφS s X; TÞ
ð
ΔPTðÞ 5 P 0; TÞ 2 P 1; TÞ 5 dX
ð
ð
2 X
X w (3.141)
1 βφ ð 1 S s X; TÞ
ð
52 lnX w 1 dX:
2 2 X
X w
3.5.3.1 Qualitative analysis of the model
The evolution of attached, suspended and strained particle profiles during
low-salinity water injection with fines migration is now analyzed. The
trajectories of salinity and particle fronts in areas A, BC, and D are pre-
sented in Fig. 3.21A. Fig. 3.21B shows the different flow zones.
The initially mobilized fines move with the particle speed α and are
captured by straining. The fines removed from area A move in zone 3.
Movement of fines from zone 3 continues into zones 4 and 5 after by-
passing of zone 3 by the salinity front; the fines propagation continues
with speed α.
The fines initially detached in area BC also move with the particle
speed α in zone 1; the time decrement in the formula for suspended con-
centration in zone 1 is the same as that in zone 3. Zone 1 disappears at
moment T 1 . The fine particle propagation from zone 1 continues into
zones 6, 7, and 8 after by-passing of zone 1 by the salinity front. The par-
ticle speed and straining probability remain the same.
No particles are mobilized in area D; thus, there is no suspended par-
ticles in zone 0.
The maximum retention curve for γ 5 γ I lies above the curve for
γ 5 γ J , so the salinity front releases the attached fines. As it follows from
particle mass balance conditions at the salinity front, given by formula
(Eq. (3.106)), the released suspension concentration is equal to vertical
1
distance between the curve S a , given by first formula of Eq. (3.136),
and the maximum retention curve for γ 5 γ J , times (α-1) 21 .
There are no attached particles in area A, both maximum retention
concentrations for γ 5 γ I and γ J are zero, so no particles are released