Page 313 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 293

during the initial period of the filter cake formation. The cake formation
models developed in this section can be used for predicting the effects
of the compressible filter cakes involving the drilling muds and fractur-
ing fluids.
The applications of the improved models are illustrated by typical
case studies.

Radial Filtration Formulation

Consider that a slurry is applied to the inner surface of a drum filter
and the filtrate leaves from its outer surface (see Figure 12-4). The model
developed here is also equally applicable for the reverse operation. The
filter cake is located between the filter inner surface radius r w(cm) OVer
which the cake is formed, and the slurry side cake surface radius r c(cm)
and its thickness is denoted by h = r w-r c. The external surface radius of
the filter from which the filtrate leaves is r e(cm) and the filter width is
indicated by w(cm), such that the area of the inner filter surface over
which the cake is formed is 2nr ww. The slurry flows over the cake
surface at a tangential or cross-flow velocity of v f(cm/s) and the filtrate
3>
3
flows into the filter at a filtration velocity of M / (cm /cm s) normal to
the filter face due to the overbalance of the pressure between the slurry
and the effluent sides of the filter. The flowing suspension of particles
and the filter cake (solid) are denoted by the subscripts / and s, respec-
tively. The carrier phase (liquid) and the particles are denoted, respectively,
by / and p. Following Tien et al. (1997), the slurry is considered to
contain particles larger than the filter medium pore size that form the filter
cake and the particles smaller than the pore sizes of the filter cake and
the filter medium, which can migrate into the cake and the filter to deposit
there. All particles (small plus large) are denoted by p, and the large
and small particles are designated by pi and p2, respectively.
Civan (1998b, 1999b) developed the filtration models by considering
the cake-thickness averaged volumetric balance equations for
1. The total (fine plus large) particles of the filter cake;
2. The fine particles of the filter cake;
3. The carrier fluid of the suspension of fine particles flowing through
the filter cake; and
4. The fine particles carried by the suspension of fine particles flowing
through the filter cake.

The radial mass balances of all particles forming the cake, the small par-
ticles retained within the cake, the carrier fluid, and the small particles
suspended in the carrier fluid are given, respectively, by (Civan, 1998b):