Page 104 - Reservoir Formation Damage

Permeability Relationships 87

with different values of the parameters a, ra, d t, and d h. Chang and Civan
(1991, 1992, 1997) used the critical particle diameter, \d p] , necessary
for pore throat jamming, determined according to the criteria described
in Chapter 8.
For applications with multiphase flow systems, Liu and Civan (1993,
1994, 1995, 1996) used a simplified empirical equation for permeability
reduction in porous media as:

(5-33)

where K 0 and <|> 0 are the reference permeability and porosity, K f, is the
residual permeability of plugged formation, and / is a flow efficiency
factor given by:

(5-34)

where i and / denote the species and phases, k f are some rate constants
and e u are the quantity of the pore throat deposits. The instantaneous
porosity is given by:

(5-35)

where (e, /) is amount of surface deposits.

The Plugging-Nonplugging Parallel Pathways Model

The porous media realization is based on the plugging and nonplugging
pathways concept according to Gruesbeck and Collins (1982). Relatively
smooth and large diameter flowpaths mainly involve surface deposition
and are considered nonplugging. Flowpaths that are highly tortuous and
having significant variations in diameter are considered plugging. In the
plugging pathways, retainment of deposits is assumed to occur by jam-
ming and blocking of pore throats when several particles approach narrow
flow constrictions. Deposits that are sticky and deformable usually seal
the flow constrictions (Civan, 1990, 1994, 1996). Therefore, conductivity
of a flow path may diminish without filling the pore space completely.
Fluid seeks alternative flow paths until all the flow paths are eliminated.