Page 90 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

72 Thomas Russell et al.

Figure 3.3 Torque balance of electrostatic, gravity, lift, and drag forces (F e , F g , F L , and
F d ) and lever arms l n and l d for attached particles.

Figure 3.4 Fine-particle-capture mechanisms in a single pore.

Fig. 3.4 shows different mechanisms of particle capture by porous
rock: size exclusion in thin pores, bridging, electrostatic attraction, gravity
segregation, and diffusion into dead-end pores and stagnant flow zones.
The traditional colloidal flow model assumes simultaneous attachment
and detachment of colloidal particles in porous media (Bradford et al., 2003;
Bradford and Torkzaban, 2008; Sharma and Yortsos, 1987; Tufenkji, 2007):

@σ a
5 λcU 2 k det σ a ; (3.2)
@t
where the attachment rate is proportional to the advective flux of sus-
pended particles cU, and the detachment rate is proportional to the
attached concentration. Here, c and σ a are the suspended and attached
concentrations, U is the Darcy’s velocity, λ is the filtration coefficient,
which is the particle capture probability per unitary length of its trajec-
tory, and k det is the kinetic detachment coefficient, which is the reciprocal
of the reference detachment time.