Page 160 - Petrophysics

PERMEABILITY-POROSITY RELATIONSHIPS 133

the case. Equation 3.63 should be used only in the presence of clastic
sediments. A similar expression was derived by Timur [34]:

44.4
k = 0.136- (3.64)
Swi

where permeability is in mD and and @ are expressed in percentages.
Equation 3.64 is independent of the type of hydrocarbon present in the
porous medium.
It is important to emphasize that Equations 3.60 through 3.64 are
empirical. They are commonly used to obtain an estimate of permeability
distribution from well log data. If porosity and irreducible water
saturation are used in fractional form, Equation 3.64 has the form:

(3.65)

Langnes et al. presented another empirical equation that was used
successfully for sandstones [35]. It relates the specific surface area per
unit of pore volume, svP, to the porosity 4 (fractional), permeability k
(in millidarcies), and formation resistivity factor FR &Atw, where &
is equal to the electric resistivity of a formation 100% saturated with
formation water and Rw is equal to the formation water resistivity):

(3.66)

The formation resistivity factor captures the effects of grain size, grain
shape, grain distribution, and grain packing.

EXAMPLE

An oil-bearing core sample recovered from a clean sandstone formation
has a porosity of 24% and an irreducible water saturation of 30%.
Estimate:

(a) The permeability of the core sample using the Wyllie and Rose
correlation (Equation 3.63) and compare the result with that obtained
from the Timur correlation (Equation 3.64); and
(b) The average grain size.