Page 105 - Reservoir Formation Damage

88 Reservoir Formation Damage

Then the permeability diminishes even though the porosity may be
nonzero. Another important issue is the criteria for jamming of pore
throats. As demonstrated by Gruesbeck and Collins (1982) experimentally
for perforations, the probability of jamming of flow constrictions depends
strongly on the particle concentration of the flowing suspension and the
flow constriction-to-particle diameter ratio.
The pore plugging mechanisms are analyzed considering an infini-
tesimally small width slice of the porous core. The total cross-sectional
area, A, of the porous slide can be separated into two parts: (1) the area
A p, containing pluggable paths in which plug-type deposition and pore
filling occurs, and (2) the area, A np, containing nonplugging paths in
which nonplugging surface deposition occurs. Thus, the total area of
porous media facing the flow is given by:

A - A p + A np (5-36)

The fractions of the bulk volume containing the plugging and nonplugging
pathways can be estimated by (Civan, 1995, 1996):

f = (5-37)

A
fnp = npI A ~ §np/$ (5-38)
where <|> p, § np, and <() denote the porosities of the plugging, nonplugging,
and overall flow pathways.
Thus, by definition:

/„+/«, = ! (5-39)

The fraction of the plugging pathways is a characteristic property of
porous media and the particles of the critical size, comparable or larger
than the pore throat size (Gruesbeck and Collins, 1982; Schechter, 1992).
As explained in Chapter 8, the pore size distribution of the porous
medium and the size distribution of the particles determine its value.
However, its value varies because the nonplugging pathways undergo a
transition to become plugging during formation damage.
The volumetric flow rate, q, can also be expressed as a sum of the flow
rates, q p and q np, through the pluggable and nonpluggable paths as:

(5-40)
q = q p + q np