Page 172 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

148 Thomas Russell et al.

And the outlet concentration is treated as the accumulated outlet
concentration:
ð
C acc 5 α C 1; yð Þdy: (3.164)

These two datasets can be tuned using any optimization algorithm.
To demonstrate the applicability of the model, one experiment on
artificial sandstone cores is presented. The cores comprised of 5% kaolin-
ite and 95% chemically-washed silica sand. The methodology for the test
can be found in the work of Russell et al. (2017).
The five model parameters α, ε, Λ, β, and Δσ are tuned here using a
least-squared genetic algorithm implemented in MATLAB. The experi-
mental data and tuned model results are presented below in Fig. 3.25 and
the resulting model parameters are given in Table 3.11.
The model fit shows good agreement with the experimental data,
2
achieving a value for R higher than 0.95. Note that although the drift
delay factor is not equal to one, modeling fines migration without the
detachment delay factor would result in a prediction of permeability sta-
bilization after the injection of less than 10 pore volumes. The delay in
detachment accounts for the remainder of the lengthy stabilization time.

3.6.4 Semianalytical model for axisymmetric flow

As in Section 3.5.3, the equations for fines migration can be extended to
axisymmetric radial flow for the purpose of predicting well behavior.
With the inclusion of delayed detachment, the system of
Eqs. (3.114 3.118) is modified to include a nonequilibrium expression.
The problem of delayed detachment is more nuanced in radial coordi-
nates. In corefloods, changes to salinity or injection rate are controlled;
thus, to study the underlying processes, only one of these variables is
changed during any one injection cycle. This allows the modeling to be
done with one of the analytical solutions presented previously
(Section 3.3 for changes to velocity, and Sections 3.5 and 3.6.2 for
changes to salinity). In radial flow, the fluid velocity varies with distance
from the wellbore. With low-salinity injection, particle detachment will
result from both changes to velocity and fluid salinity. In Section 3.6.1,
it was reasoned that the delay in detachment was only appropriate
when particle detachment was induced by changes to salinity. As such,
detachment during radial injection should comprise of both instant and
delayed detachment.