Page 315 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 295

The variation of the filter cake thickness (cm) h = r w - r c can be cal-
culated using the variable radius, r c = c (t], of the slurry side filter
r
cake surface.
For many practical applications, it is reasonable to assume that the
particles and the carrier fluid are incompressible. The volumetric retention
rates of the large and small particles are given, respectively, by:

(12-93)
N p2s = R p2s/P p
The volumetric concentration (or fraction) of species / in phase 7, the volume
fraction of species i of phase j in the bulk of the cake system, and the
superficial velocity of species / of phase j are given, respectively, by:

(12-94)
G ij=c ij/p i
e, 7=e. a fj (12-95)

(12-96)
u ij=u j<5 ij
t denotes the time; ^, ¥ p2j, and != p2l are the cake-thickness-average
porosity, the fine particle volume fractions of the cake matrix and the
suspension of fine particles flowing through the cake matrix, respectively;
e
( P i)slurry is the volume fraction of the total (fine plus large) particles in
the slurry; and (ui) slurry and (ui) flltrate denote the volume fluxes of the
carrier fluid entering and leaving the filter cake, respectively.
Substituting Eqs. 12-92 to 12-96 into Eqs. 12-87 to 12-90 leads to
the following volumetric balance equations, respectively (Civan, 1999b):

(12-97)
dt

e p2s] = 2r cN° p2s (12-98)
dt

(12-99)
= 2r («,) . -2r w (w,) _,
c
w
\ ' > slurry \ ' Ifilrate