Page 233 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 213

where K 0 and § 0 are the initial permeability and porosity and 7 is the
flow efficiency factor, which is a measure of the fraction of the pore
throats remaining open (see Figure 10-3). Thus, when all the pore throuts
are closed, then y = 0 and K = Q, even if 0^0.
The cumulative volume of fluid injected at x = 0, expressed in terms
of the initial undamaged pore volume, is given by

(10-166)

is the injection volumetric flux.
u 0
The cumulative fines production at x =• L, in the effluent is
t
dt (10-167)
Q pL
=A^<5 pLu
and are the effluent volumetric flux and particle fraction, respectively.
U L G pL
The harmonic mean average permeability of the core of length L is
calculated by

L
K =L \(\IK)dx (10-168)
/ J

The linear flow model presented above can be converted to the radial
flow model by the application of the transformation given by (Ohen and
Civan, 1991):

x = ln(r/r w) (10-169)

r and r w denote the radial distance and the well bore radius, respectively.

Model Assisted Analysis of Experimental Data

Without the theoretical analysis and understanding, laboratory work can
be premature, because the analyst may not exactly know what to look
for and what to measure. The theoretical analysis of various processes
involved in formation damage provide a scientific guidance in designing
the experimental tests and helps in selecting a proper, meaningful set of
variables that should be measured. Having studied the various issues
involving formation damage by fines migration, we are prepared to