Page 312 - Reservoir Formation Damage

292 Reservoir Formation Damage

The large flow rates encountered during this period usually promote a
non-Darcy effect. Willis et al. (1983) investigated the non-parabolic
filtration behavior, but concluded that the non-parabolic behavior is a
result of the impairment of the permeability of porous media by invasion
and clogging by fine particles rather than by the non-Darcy flow effect.
This conclusion is justified for their experimental conditions, however,
some reported experimental data appear to involve a non-Darcy flow
effect during the initial period of filter cake buildup.
Civan (1998b, 1999b) developed linear and radial filtration models and
verified them by means of experimental data. These models are more
generally applicable because of the following salient features:

1. A cake-thickness-averaged formulation leads to a convenient and
computationally efficient representation of the filtration processes
by means of a set of ordinary differential equations;
2. The nonhomogeneous-size particles of the slurry are classified into
the groups of the large and fine particles, and the large particles form
the cake matrix and the fine particles deposit inside the cake matrix;
3. The flow through porous cake and formation, which acts as a filter,
is represented by Forchheimer's (1901) law to account for the
inertial flow effects encountered during the early filtration period;
4. The dynamic and static filtration conditions encountered with and
without the slurry flowing tangentially over the cake surface, respec-
tively, are considered;
5. The variation of the filter cake porosity and permeability by com-
paction due to the drag of the fluid flowing through the cake matrix
and deposition of fine particles within the cake matrix is considered;
6. An average fluid pressure is used to determine the fluid drag force
applied to the cake matrix;
7. The formulations are presented for general purposes, but applied for
commonly encountered cases involving incompressible particles and
carrier fluids; and
8. The constant and variable rate filtration processes can be simulated.

The model presented in this section incorporates empirical constitutive
relationships for the permeability and porosity variations of compressible
cakes retaining fine particles. The simulation of a series of filtration
scenarios are presented to demonstrate the parametric sensitivity of the
model. It is determined that permeability impairment by fine particles
retainment and pore throat clogging in the filter cake is increasingly
induced by cake compression. It was also determined that constant
pressure filtration limits the filtrate invasion more effectively than con-
stant rate filtration and the non-Darcy flow effect is more significant