Page 180 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 155

A simplified form of the critical retention function can be used to
demonstrate the effect of the delay in detachment on well injectivity. For
example, suppose that the maximum velocity present in the critical reten-
tion function:
8
!
2

>
< σ aI 1 2 U ; U , U m γðÞ
σ cr U; γð Þ 5 U m γðÞ ; (3.196)
>
0; U . U m γðÞ
:
decreases linearly with decreases in salinity. As such, the critical retention
function will be lower for lower salinities, as predicted by the qualitative
analysis of the torque balance outlined in Section 3.2. The resulting form
of the critical retention function in dimensionless coordinates is:

d
S cr U; γ 5 a 1 2 ; (3.197)
0

0 2
XU m0 1 U m1 2U m0 Þγð ð Þ
where,
2
q
σ 0
a 5 ; d 5 ; σ 0 5 σ cr U-0; γÞ: (3.198)
ð
φ 2πr e
This form of the critical retention function provides a simple but
effective means to predict injectivity decline during low-salinity water
injection with delayed detachment.

3.6.5 Prediction of injection well behavior
A calculation of injectivity is performed to demonstrate the behavior of
the model, primarily reflecting the effect of the delay factor. The results
are shown in Fig. 3.26. The values of the other parameters used in these
calculations are given in Table 3.13.
Fig. 3.26 clearly demonstrates the impact of the delay factor τ.
Increasing the delay factor results in a longer stabilization time for the
impedance, but does not change the stabilized value.
The computation of impedance varies significantly with the maximum
retention function applied. To illustrate the effect of including a delay in
detachment, a simplified σ cr model is presented. To model injectivity
decline for the purposes of industrial applications, it is possible that a
more rigorous model for particle detachment would be required.