Page 288 - Reservoir Formation Damage

268 Reservoir Formation Damage

(12-5)

where k' and n denote, respectively, the consistency constant and flow
index. The critical shear-stress is dependent on various factors, including
surface roughness and particle stickiness (Civan, 1998a,b) and aging (Ravi
et al., 1992) and it should be measured directly. The deposition and
erosion rate constants depend on the properties of the particles and carrier
fluid, and the conditions of the slurry, such as particle concentration, flow
rate, and pressure.
Ravi et al. (1992) have determined that the following equation proposed
by Potanin and Uriev (1991) predicts the critical shear stress with the same
order of magnitude accuracy of their experimental measurements:

(12-6)

where H = 3.0x10 13 erg is the Hamaker coefficient, d(cm) is the aver-
age particle diameter, and /(cm) is the separation distance between the
particle surfaces in the filter cake. However, the values calculated from
Eq. 12-6 is only a first order accurate estimate because Eq. 12-6 has
been derived from an ideal theory. The ideal theory does not take into
account the effect of the other factors, such as aging (Ravi et al., 1992),
surface roughness, and particle stickiness (Civan, 1996), on the particle
detachment. Therefore, the actual value of the critical shear stress may
be substantially different than that predicted by Eq. 12-6 using the particle
size and separation distance data. Hence, Ravi et al. (1992) recommend
experimental determination of the critical shear stress.
U(i s-i cr] is the Heaviside step function [U(i s—i cr) = 0 when
T 5 < T and £/(T 5 -T cr ) = l when T, >T C J.
\e s pJ is the mass of particles contained per unit bulk volume of the
slurry side cake surface. The erosion rate is related also to the particle
content of the cake (e. p n } and erosion cannot occur if there is no cake,
\ A "'C
p p J = 0 . Here, the cake properties are assumed constant.
(e s

==€=, p = constant (12-7)

Therefore, k e and (<E S p p) can be combined into one coefficient as
(Civan, 1999a)

k.= (12-8)