Page 107 - Reservoir Formation Damage

90 Reservoir Formation Damage

u p=uK p/K (5-50)

u np=uK np/K (5-51)

Let <|> and <j) K denote the initial pore volume fractions of the
plugging and nonplugging pathways of the porous media (Civan, 1995)
and £ p and £ np represent the fractions of the bulk volume occupied by
the deposits in the respective pathways. Thus, the instantaneous porosities
in the plugging and nonplugging pathways are given by:

Po (5-52)

$ np=$n Po-z np (5-53)

Total instantaneous and initial porosities are given, respectively, by:

(b = (b + (b (5—54)

(|) = (j> + cj) (5—55)

The total deposit volume fraction and the instantaneous available porosity
are given by:

(5-56)
e = e p + z np
(J) = (|> o — e (5—57)

The permeabilities of the plugging and nonplugging pathways are given
by the following empirical relationships by Civan (1994) by generalizing
the expressions given by Gruesbeck and Collins (1982):

K = (5-58)

and

(5-59)