Page 101 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 83

Figure 3.6 Typical forms for total potential energy profile for high- and low-salinity
water (V: potential energy of interaction, h: particle-grain separation distance).

profiles are presented in Fig. 3.6. The total force acting on the attached
particle is opposite to the gradient of the total energy:
@V
F e 52 ; (3.14)
@h

where F e is the total electrostatic force, and V is the total interaction
energy.
In equilibrium, the system will tend to a state in which the acting
force is zero. These positions are either at maxima, minima, or at infinite
separation distance. Maxima are unstable equilibrium points because slight
variations in the separation distance will result in forces driving the parti-
cle away from the maximum. Minima, however, are stable points, because
the energy profile on either side of the minima will drive particles
back toward the minimum. Thus, when a particle is attached, it is consid-
ered to either be in the primary or the secondary minimum. When
attempting to leave either of these minima (increasing the separation dis-
tance), the particles will encounter a positive potential energy gradient,
and hence a negative, or attractive, force. The maximum force experi-
enced during this passage, located at the inflection point on the potential
energy profile, is taken as the electrostatic force used in the torque balance
equation, outlined above.