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Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 141

criteria for attached particles. In the following section, it will be proposed
that changes to the fluid salinity may not result in an immediate detach-
ment of particles. A nonequilibrium relation between the attached con-
centration and the critical retention function will be introduced to model
this additional phenomenon.

3.6.1 Introduction of a delay in detachment

First, it is necessary to revisit the criteria for detachment outlined in
Section 3.2. The primary forces acting on the particle are the hydrody-
namic drag force and the electrostatic force. Increasing the velocity will
increase the former; whereas, decreasing the salinity will decrease the lat-
ter. Both changes will result in shifting the mechanical equilibrium of
attached particles toward detachment. Under the assumption of fluid
incompressibility, changes to injection rate will naturally result in an
immediate change to the acting hydrodynamic force. Consequently, the
assertion that the attached concentration can instantaneously be deter-
mined from the critical retention function holds:
σ a x; tð Þ 5 σ cr UðÞ: (3.143)

Changes to salinity are potentially more complex. DLVO theory states
that the electrostatic force is a function of the type and concentration of
ions in the confined, interparticle region between the attached particle
and the grain surface. Ions in this region will form an equilibrium with
the ions in the bulk solution; however, the ionic concentration in these
two regions will generally not be equal. The difference arises due to the
tendency of charged ionic species to surround oppositely charged surfaces
(Israelachvili, 2011). Previous formulations of fines detachment due to
salinity have relied on the assumption that changes to the bulk salinity
recorded at any point in the core immediately translate into changes in
the salinity in the interparticle region for any attached particles. The
transfer rate of ions between the bulk solution and the interparticle region
will however be finite, and the resulting delay between changes to salinity
and the electrostatic force may have significant impacts on particle
detachment.
Due to the proximity of the particle to the attached grain, advective
flux is likely to be low, and ion transfer will be dominated by diffusion.
Mahani et al. (2015) investigated the similar problem of ion diffusion
between an oil droplet and clay and demonstrated that the exceedingly