Page 294 - Reservoir Formation Damage

274 Reservoir Formation Damage

in which (3 is an empirically determined coefficient.
For constant rate filtration, Eq. 12-11 subject to Eq. 12-14 can be
integrated numerically for varying shear-stress T s. When the shear-stress
is constant or does not vary significantly, an analytical solution can be
obtained as (Civan, 1999a):

= (Aq-B)t (12-42)

in which fi = 0 because T = 0 for static conditions and 5^0 because
t * 0 for dynamic conditions. The cumulative filtrate volume is given by,
for both the static and dynamic filtration

Q = qt (12-43)
Then, the pressure difference (p c-p e) or the slurry injection pressure
p c, when the back pressure at the effluent side of the porous filter media
is prescribed, can be calculated by Eq. 12-19. The following con-
p e
ventional filtration equation (Hermia, 1982; de Nevers, 1992) can be
derived by invoking Eq. 12-43 into Eq. 12-40:

(12-44)
Q q 0

Radial Filter Cake Model

A schematic of the formation of a filter cake over the sand face during
over-balanced mud circulation in a wellbore is shown in Figure 12-3.
Figure 12-4 is a quadrant areal view of the problem. The radii of the mud
slurry side cake surface, the sand face over which the cake is built up,
and the external surface considered for the region of influence are denoted
r
by r c, w an d r e, respectively. The formation thickness is h.
The particle mass balance equation is given by (Civan, 1994, 1998a)

(12-45)

The filter cake thickness is given by

5 = r, - (12-46)

is given by Eq. 12-9. The slurry shear-stress at the cake surface is
R ps
given by the Rabinowitsch-Mooney equation (Metzner and Reed, 1955)