Page 138 - Petrophysics

PERMEABILITY-POROSITY RELATIONSHIPS 111

Thus, for a bundle of tortuous capillary tubes, Poiseuille’s law becomes:

Combining Equation 3.22 with Equation 3.11 and using the same
approach as above, one can show that Equations 3.14, 3.18, and 3.19
respectively become:

k= (2) @ (3.23)

(3.24)

(3.25)

Wyllie and Spangler suggested that the factor 2 be replaced by a more
general parameter, namely, the pore shape factor Kps [18]. Carman
reported that the product Kps7 may be approximated by 5 for most
porous materials [ 191. Equation 3.25 for porous rocks can then be written
as follows:

Equation 3.26 is the most popular form of the Kozeny equation, even
though in actual porous rock Kps7 is variable and much greater than 5.

EXAMPLE

A sandpack of uniform fine grains has an effective porosity of 0.2.
The average grain size diameter is approximately 1/8 mm. Calculate the
permeability of this unconsolidated sandpack.

SOLUTION

The specific surface area of the grains can be estimated, assuming that
the grains are spherical, as follows:

6
SVgr = -
dgr