Page 214 - Petrophysics 2E

PERMEABILITY-POROSITY RELATIONSHIPS 187

Although it has been developed primarily for permeability zonation, the
technique is general and can be applied to reservoir properties other than
permeability. The reservoir zonation technique is a twepart operation.
Permeability data from the top to the bottom of the strata of a
single well are divided into zones. These zones are selected such that
the variation of permeability within the zones is minimized and
maximized between the zones. The statistical equations used to zone
the permeability data are:

(3.132)

where:

szz = variance between the zones.
NZ = number of zones
nk = total number of permeability data in the strata.
NK = number of permeability data in the ith zone.
kij = permeability data.
i = summation index for number of zones.
j = summation index for the number of data within the zone.

The variance within any zone, sz, is computed from:

and the zonation index, Iz, is:

s,
Iz=l-- (3.134)
SZZ
This index is the criterion used to indicate the best division. Iz, which
ranges between 0 and 1, indicates how closely the division corresponds
to homogeneous zones. The closer Iz is to 1, the more homogeneous are
the zones. Any negative value of Iz must be replaced by zero in order to
conform to the definition of Iz.
The zonation of individual wells is a multi-step procedure:

(a) First, the permeability data, in their original order of depth, are
divided into all possible combinations of two zones. Then, the