Page 206 - Petrophysics 2E

PERMEABILITY-POROSI"Y RELATIONSHIPS 179

- n - 29
kH = - 1 1 1 1 1 = ~3 mD
(.' 1=1 d) -+-+-+-+... +-
4
220
7
130
90
The harmonic averaging technique yields, as expected, the lowest value
of average permeability. In this case, the difference between the three
averages is very significant, implying that the formation is extremely
heterogeneous. Another reason for this large difference is that no values
of permeability were cutoff. Generally the amount of cementing material
is high for low permeability values, and low for very high permeability
values.
(3) The effective permeability of this formation is estimated from
Equation 3.124.
From Equations 3.125, we calculate the geometric mean of the natural
log of the core-derived permeability values:

k~ = -j/lnkl Ink2 lnk3.. .Ink, = (1.9855 x lo")& = 4.275 mD

To calculate the variance 0: we need to use Equations 3.126 and 3.127:

- Chki 139.54
Ink=--- =-- - 4.812 mD
n 29
x(ln ki - In k)2 x(ln ki - 4.812)2 124.51
-
---
02 = - - - 4.3
n 29 29
Using the geometric mean of the natural log of k values, the effective
permeability is:

ke = (1 + 7) exp [4.275] = 123 mD

(4) The Dykstra-Parsons coefficient is obtained from Equation 3.115.
Using the same approach as in the previous example, we find:

k84.1 = 8.38 mD was obtained by interpolating in Table 3.13 or
Figure 3.53.

The Dykstra-Parsons coefficient is very high, indicating an extremely
heterogeneous reservoir.