Page 116 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

98 Thomas Russell et al.

(A) T
T b
1/α 1
X = α 1 T
T a

0 1 X
(B) C
T = 0
1
T a

T b

0 1 X
(C) S s
T b

T a
T = 0
0 1 X
Figure 3.11 Solution space (A) and concentration profiles for the suspended (B) and
strained (C) concentrations for the derived analytical solution for fines migration (X:
dimensionless linear coordinate, T: dimensionless time, C: dimensionless suspended
concentration, S s : dimensionless strained concentration).

All detached particles move through the core with velocity α, which
defines the slope of the characteristics along which Eq. (3.48) is solved.
Ahead of the particle concentration front (X . αT), the suspended
particles are uniformly distributed along the core. This follows from the
fact that each particle moves with the same velocity and has the same
probability of capture via straining. This uniform distribution decreases
monotonically with time as the particles are captured in small pore
throats. As a result of the uniform distribution of C, and the constant
straining rate, the strained concentration ahead of the concentration front
is similarly independent of X.
Behind the concentration front (X , αT), all suspended particles have
either been captured, or transported further into the core. As such, the