Page 317 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 297

(12-108)

(12-109)
l
l
V > slurry \ > filtrate

(12-110)
filtrate

Eqs. 12-107 through 110 can be solved numerically, subject to the initial
conditions given by:

r
vy, i
^-p2.s
^-/72/
^ J. z,
111 j
•*c = r w' "E" „ ="H" — O f = 0 (19—111^
w
The volume fractions of the filter cake solids and pore fluid can be
expressed in terms of the cake porosity, respectively, as
€,=1-0 (12-112)
€/=E / +e p2; =0 (12-113)

3
3
where (j) is the average cake porosity (cm /cm ). The following expres-
sions for the small particle volume flux and mass per carrier fluid volume
can be written according to Eqs. 12-94 through 96, respectively, as:

"*2/ = «/ e P2 //e,= «,<Wp p (12-114)

C U p2/ =O C G „,/£, v ^ AJ^
n2-11*rt
1
„,
c
i
rp p2// /
Note that Eqs. 18, 28, and 24 of Corapcioglu and Abboud (1990)
correspond to the present Eqs. 12-103, 12-109, and 12-106, respectively,
with some differences. Equation 12-103 simplifies to their Eq. 18,