Page 103 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 85

and temperatures and low-salinity water are favorable conditions for parti-
cle mobilization (You et al., 2014).

3.2.2 Using the torque balance to derive expressions
for the maximum retention function
The principle of particle mobilization in porous media due to perturba-
tion in the torque balance leads to the development of a macroscale
mathematical model for attached particle concentration. Such an expres-
sion can be used to model suspension transport in porous media with
particle detachment given changes to the particle mechanical equilibrium
(Bedrikovetsky et al., 2011a).
The classical approach to modeling particle detachment is to imple-
ment a first-order rate equation to capture the detachment kinetics.
Several authors have, however, demonstrated that changes to flow rate or
salinity result in seemingly instantaneous changes to the attached concen-
tration. A more thorough discussion of the appropriateness of particle
detachment kinetics will be presented in Section 3.6.
Nonetheless, regardless of whether kinetics is deemed important in
the formulation of particle detachment, an equilibrium function is
required which describes the final attached concentration. Such a func-
tion should recognize the changes to attachment conditions governed by
the dependencies of the acting forces outlined above. This function will
be referred to here as the maximum retention function.
The classical model to describe particle attachment and detachment
accounts for particle detachment kinetics yielding to an asymptotical sta-
bilization for retention concentration and permeability when time tends
to infinity, Eq. (3.2). Nonetheless, the fines mobilization and permeability
increase after sharp increase in flow rate or shocks of salinity alteration
(Jaiswal et al., 2011; Khilar and Fogler, 1998; Ochi and Vernoux, 1998;
Oliveira et al., 2014; Sarkar and Sharma, 1990). As the traditional model
fails to reflect the prompt permeability and particle release observed in
many laboratory experiments, alternative models capable of modeling the
instant particle release have to be applied to calculate the maximum
retention concentration.
In the following sections, two models for the maximum retention
function will be presented. The first assumes that mono-sized particles
form a multilayer internal cake within pores. The second recognizes a
distribution in particle sizes, but restricts particle attachment on the pore
wall to a single layer.