Page 223 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 203

These values can be determined experimentally for a given porous media
and the particle size distribution. e p and £ np represent the fractions of
the bulk volume occupied by the deposits. Thus, the instantaneous
porosities are:

(10-93)
ty p = § p -£ p
=
$np §np -Znp (10-94)
The fractions of the bulk volume containing the plugging and nonplugging
pathways can be approximated, respectively, by:

L=$ DI$ (10-95)

fnp=$np/§ (10-96)

However, Gruesbeck and Collins (1982) assume a constant value for f p
(and therefore for f np =l-f p), which is a characteristic of the porous
medium and the particles. Total instantaneous and initial porosities are
given, respectively, by:

ty = ty p+ty (10-97)

(10-98)
§ 0=ty po+$ np
The total deposit volume fraction and the instantaneous available porosity
are given, respectively, by:
(10-99)
e = £ p +e n p
<|) = (|) 0-e (10-100)

The rate of deposition in the plugging pathways is given by assuming
the pore filling mechanism:

dz p/dt = k pUpG p<$> p (10-101)

e p=e/ v t = 0 (10-102)

where <5 p is the volume fraction of the particles flowing through the
plugging pathways, k p=Q when t < t p. t p is the time at which the pore
throats are blocked by forming particle bridges and jamming. This occurs