Page 133 - Petrophysics 2E

106 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

1000

100

? 10
J

I

0.1
0 5 10 15 20 25
Porosity, Fraction
Figure 3.1 1. Permeability-porosity relationship

Chilingarian showed that the granulometric composition of sandstones
influences the relationship between permeability and porosity [ 141.
Figure 3.12 is a semilog plot of permeability versus porosity for (1) very
coarse-grained, (2) coarse and medium grained, (3) fine-grained, (4) silty,
and (5) clayey sandstones. Figure 3.13 shows typical permeability and
porosity trends for various rock types. Such a relationship is very
useful in the understanding of fluid flow through porous media. Many
correlations relating permeability, porosity, pore size, specific surface
area, irreducible fluid saturation, and other variables have been made.
Some of these relationships are presented here for the sole purpose
of enabling the reader to form a reasonable understanding of the
interrelation of the rock properties in petroleum reservoirs.

KOZENY CORRELATION

Kozeny derived one of the most fundamental and popular correlations
expressing permeability as a function of porosity and specific surface
area [ 151. Consider a porous rock sample of cross-sectional area A and
length L as being made up of a number, n, of straight capillary tubes
in a parallel, with the spaces between the tubes sealed by a cementing
material. If the capillary tubes are all of the same radius r (cm) and length
L (cm), the flow rate q (cm3/s) through this bundle of tubes, according
to Poiseuille’s equation, is:

(3.10)

where the pressure loss AP over length L is expressed in dynes/cm2.