Page 320 - Reservoir Formation Damage
P. 320
300 Reservoir Formation Damage
where h is the formation thickness. Thus, invoking Eq. 12-125 into
Eq. 12-124 yields
M- (q
(12-126)
2nhk(r
The pressure differences over the filter cake and porous media can be
expressed by integrating Eq. 12-126, respectively, as (Civan, 1999b):
1 1
(12-127)
2
(2nh) r. r,.,
In * I (12-128)
(2nh) 2
2nhk f
The densities and instantaneous flow rates of the suspensions of fine
particles flowing through the cake matrix and porous formation are
assumed the same. Then, adding Eqs. 12-127 and 12-128, and rear-
ranging and solving, yields (Civan, 1999b) for Darcy flow \fo f =p c =0j:
(12-129a)
and for non-Darcy flow:
= —-£— = Mslurr
2nrji
(12-129b)
2a
in which
^- P J__l (12-130)
£. r,, r,.. r.
