Page 52 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

34 David A. Wood and Bin Yuan

Figure 2.7 Forces acting on a fines particle attached to a pore wall (i.e., adsorbed)
within a reservoir rock saturated with formation fluid. Modified after Bedrikovetsky
et al. (2012).

Equation 2.1 can be used to calculate the dimensionless erosion
number, ε, which is the ratio between detaching and attaching forces
(Eq. (2.2)).

F d l d 1 F l l n
ε 5 (2.2)
ðF e 1 F g Þl n
In-situ (nonswelling) fines will only be mobilized if the detachment
forces exceed the attachment forces, i.e., where ε exceeds the electrostatic
force. The maximum retention concentration of particles σ a for specific
flow and salinity conditions can then be expressed as Eq. (2.3).

σ a 5 σ cr ðεðU; γÞÞ (2.3)
where: σ cr is the maximum volumetric concentration of captured parti-
cles, U is formation fluid velocity, and γ is fluid salinity. This equation
can be evaluated for γ i (formation fluid salinity) and γ o (and injected fluid
salinity) to evaluate the impacts of LSWF on particle retention and
calculate the concentration of fines released (Δσ). In a large reservoir vol-
ume, it is reasonable to assume that the concentration of strained particles
(σ s ) that plug pore throats is approximately the same as the concentration
of fines released (Δσ) during LSWF (Eq. (2.4)).