Page 195 - Petrophysics 2E

168 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

while the harmonic averaging method will yield the lowest average
permeability value. Thus:

Tehrani et al. [59] investigated the practicality of these three averaging
techniques in two and three dimensional flow problems. They showed
that although in some heterogeneous reservoirs the geometric averaging
method yields representative values of the effective permeability, there
are many field cases in which none of the three averaging techniques
gives satisfactory results.
In two or three dimensional heterogeneous flow systems, a combin-
ation of these three averaging techniques is necessary. For flow into a
well in a two dimensional layered system, the arithmetic average for
horizontal permeability, kr, and the harmonic average for the vertical
permeability, kv, are used to estimate the anisotropy index, IA = kr/kv,
from Equation 3.96.
The average radial or horizontal permeability, kr, is best determined
from a pressure buildup or drawdown test. The average radial permea-
bility of a heterogeneous and anisotropic system is estimated from:

kr = Jkxky - k$ (3.123)

Where k,, ky, and kW are components of the symmetrical permeability
tensor aligned with the coordinate system. These components are best
determined from a multiwell interference test. Three observation wells
located on different rays extending from the active well, which is located
at the origin of the coordinate system, are necessary to calculate k,, ky,
and kw.

Effective Permeability from Core Data
The effective permeability, obtained from core data, may be estimated
from [57,58]:

ke = (1 + 3) exp [&I (3.124)

where k~ is the geometric mean of the natural log of permeability, i.e.:

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kG = llnkllnkzlnkj ... Ink, (3.125)