Page 164 - Petrophysics

PERMEABILITY-POROSITY RELATIONSHIPS 137

intergranular pore space, the amount of unconsolidated vugs (fractures
and solution cavities), and the presence or absence of connected
vugs [37]. Figure 3.27 is a log-log plot of the permeability-porosity
relationship for various particle size groups in the uniformly cemented
nonvuggy rocks. This plot indicates that there is a reasonably good
relation between three petrophysical parameters and, therefore, if the
particle size and the matrix porosity are known, the permeability (in
millidarcies) of the nonvuggy portion of the carbonate rock can be
estimated from:

where:

@ma = matrix porosity, fraction
A,, = grain size coefficient, dimensionless
Amcp = cementation-compaction coefficient, dimensionless.

The values of these coefficients are related to the average particle
diameter de as follows:

(1) for dW less than 20 pm, the values of Agr and Am, average 1.5 x lo5
and 4.18, respectively;
(2) if d,, is n the range of 20 to 100, Agr = 2.60 x lo5 and Amcp = 5.68;
and
(3) for d,, greater than 100 pm, the values of A,, and Amcp are 8.25 x 10'
and 8.18, respectively.

If the distribution of compaction or cementation is not uniform, the
constant Amcp will be affected. Patchy cementation tends to yield higher
values of Amcp, thus reducing the permeability.
To quantlfy the effect of unconsolidated fractures and cavities on the
inter-particle porosity, Lucia examined a large number of carbonate rocks
and measured visually the fraction of the total matrix porosity due to these
types of vugs [9]. He found that their effect is to increase the interparticle
matrix porosity with little or no increase in the permeability of the matrix.
The following procedure is suggested for estimating the permeability in
carbonate rocks containing unconnected vugs:

1. Measure the total porosity (interparticle and unconnected vugs), Ot,
from well logs or core analysis.
2. Estimate visually unconnected vug porosity, 0".