Page 288 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Organic Deposition 259

conductivity and permeability reduction even when a large fraction of
nonplugging pathways still remain intact. Note that the distinction
between plugging and nonplugging pathways is subjective depending
upon the size of particles relative to the average size of a pore.
Based on empirical correlations, the permeability of the plugging
pathways can be written as follows (Civan, 1994; Gruesbeck and Collins,
1982):

k p n p
5 exp 2αφ 2φ ; (6.9)
p i p
k pi
For nonplugging pores, the permeability ratio is expressed as:
! n np
φ
k np np
5 ; (6.10)
k npi φ np
i
where α, n p ; and n np are constant fitting parameters.
Thus, total permeability reduction in porous media can be expressed
as:

k φ np ! n np
n p
5 f p exp 2αφ 2φ ; (6.11)
p i p 1 f np φ
k i
np i
where f p and f np represent the fractions of plugging and nonplugging ini-
tial permeability values, respectively, and where their sum is one. Note
that Eq. (6.10) is identical to Eq. (6.8) when n np 5 3. In addition, exami-
nation of Eq. (6.9) reveals that permeability reduction follows an expo-
nential trend due to pore throat blockage. Fig. 6.2 illustrates permeability
reduction as a function of volumetric fraction of total deposited amount
per unit pore volume, ε, using Eqs. (6.9) and (6.10). A significant perme-
ability reduction can rapidly occur (steep reduction) when plugging path-
ways are considerable in a sample (Eq. (6.9)); on the contrary, Eq. (6.10)
predicts much smoother permeability reduction when deposition mainly
occurs along nonplugging pathways and the pore plugging mechanism is
negligible. Thus, Eq. (6.8), which is usually used to model permeability
reduction as a function of asphaltene deposition, should be modified to
account for deposition onto plugging pathways/pore throats. In practice,
when the ratio of asphaltene particle size to pore throat size is larger than
a critical value, pore blockage will have a significant effect and Eq. (6.8)
or Eq.(6.10) will not be sufficient to estimate permeability reduction.