Page 191 - Petrophysics 2E

164 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

proposed the Lorenz coefficient, LK, for characterizing the permeability
distribution [46, 501:

area ABCA
LK = (3.112)
area ADCA
The value of LK ranges from zero to one. The reservoir is considered to
have a uniform permeability distribution if LK x 1. This coefficient,
however, is not unique to a particular reservoir because different
permeability distributions can yield the same value of LK .

Dykstra-Parsons Coefficient VK
Dykstra and Parsons used the log-normal distribution of permeability
to define the coefficient of permeability variation, VK [ 5 11.

where, s and 1; are the standard deviation and the mean value of k,
respectively. The standard deviation of a group of n data points is:

(3.114)

Where k is the arithmetic average of permeability, n the total number
of data points, and ki the permeability of individual core samples. In a
normal distribution, the value of k is such that 84.1% of the permeability
values are less than 1; + s and 15.9% of the k values are less than 1; - s.
The Dykstra-Parsons coefficient of permeability variation, VK, can be
obtained graphically by plotting permeability values on log-probability
paper, as shown in Figure 3.46, and then using the following equation:

where:

k50 = permeability value with 50% probability.

k84.1 = permeability at 84.1% of the cumulative sample.

The Dykstra-Parsons coefficient is an excellent tool for characterizing
the degree of reservoirs heterogeneity. The term VK is also called the
Reservoir Heterogeneity Index.