Page 284 - Reservoir Formation Damage

264 Reservoir Formation Damage

of their convenience and the reduced computational effort. The applic-
ability of the majority of the previously reported simple analytical models,
such as by Collins (1961), Hermia (1982), and de Nevers (1992), are
usually limited to linear and constant rate filtration. However, models for
constant pressure filtration are also required for certain applications. Civan
(1998a) developed and verified improved linear and radial filtration
models applicable for incompressible cake filtration without fines invasion
at static and dynamic conditions.
Simplified models omit the internal details of the filtration processes
and, therefore, may lead to incorrect results if applied for conditions
beyond the range of the experimental data used to obtain the empirical
correlations. In many applications, the phenomenological models describ-
ing the mechanisms of the cake formation, based on the conservation laws
and rate equations, are preferred for filter cake build-up involving small
particle migration and deposition and cake compaction, because these
models allow for extrapolation beyond the range of data used to test and
calibrate the models. Chase and Willis (1992), Sherman and Sherwood
(1993), and Smiles and Kirby (1993) presented partial differential models
for compressible filter cakes without particle intrusion. Liu and Civan
(1996) developed a partial differential model for incompressible filter cake
build-up, and filtrate and fine particle invasion into petroleum bearing
rock at dynamic condition. Tien et al. (1997) have developed a partial
differential model for compressible filter cakes considering small particle
retention inside the cake at static condition. The solutions of such partial
differential models require complicated, time consuming, and com-
putationally intensive numerical schemes. To alleviate this difficulty,
Corapcioglu and Abboud (1990), Abboud (1993), and Civan (1994) have
resorted to formulations facilitating cake thickness averaging. Con-
sequently, the partial differential filtration models have been reduced to
ordinary differential equations requiring much less computational effort.
Such mathematically simplified models are particularly advantageous
because ordinary differential equations can be solved rapidly, accurately,
and conveniently by readily available and well established numerical
methods. The thickness-averaged models developed by Corapcioglu and
Abboud (1990) and Abboud (1993) consider a constant porosity and linear
cake filtration at static condition. The constant porosity assumption was
justified by their filtration experiments because they used very dilute
suspensions of particles and low pressure filtration, near the atmospheric
pressure. Their models would not be applicable for high pressure filtration
of thick slurries considered by Tien et al. (1997). Further, they assumed
the same values for the rates of deposition of the small and large particles
over the progressing filter cake surface. This assumption is invalid for
most applications.