Page 106 - Reservoir Formation Damage
P. 106
. Permeability Relationships 89
The volumetric flows and volumetric fluxes are related by the fol-
lowing expressions:
q = Au (5-41)
(5-42)
A
U
Vnp = np ip~'np (5-43)
Thus, by means of Eqs. 5-36 through 43 the total superficial flow is
expressed as (Gruesbeck and Collins, 1982):
'p p Jnp np (5-44)
Applying the Darcy law, the volumetric fluxes through the porous
media and the pluggable and nonpluggable paths can be expressed as:
(5-45)
(5-46)
(5-47)
K p and K np represent the permeabilities of the pluggable and non-
pluggable fractions of the core. Assuming that the plugging and non-
plugging paths are interconnective and hydraulically communicating, the
pressure gradients are taken equal:
(5-48)
Then, it can be shown that, the average permeability of the porous
medium is given by (Civan, 1992; Schechter, 1992):
K = f K + f K (*)—4Q^
J p p J np no \ '
and the superficial flows in the plugging and nonplugging pathways are
given respectively, by:
