Page 194 - Petrophysics

PERMEABILITY-POROSITY RELATIONSHIPS 1 67

(b) Geometric Average: In heterogeneous and anisotropic formations, a
geometric average, which assumes random distribution of the matrix, is
preferable:

According to Warren and Price, the geometric mean permeability is more
consistent with the distribution found in many porous rocks [48]. The
main weakness of the geometric mean is if one individual value of k is
zero, the entire average becomes zero. To avoid this zeroing effect in
reservoir simulation, a relatively small value is assigned to the block that
has zero permeability. It should be noted that even shale has permeability
in the order of lo-' mD.
(c) Harmonic Average: The harmonic averaging technique is best suited
for layers in series such as in composite systems. This technique is
extensively used in reservoir simulation studies where different grid cells
are in series.

(d) Weighted Average: Equations 3.1 16-3.118, assume the weight
factors, wi, are equal, and that the flow is one dimensional. If the weight
factors are not equal, then these equations become, respectively:

- n
(3.12 1)

The thickness of the formation or height of the core sample,
corresponding to each permeability is a common weighting factors for
the arithmetic and geometric means. The width of each block arranged
in series is used as a weight factor in harmonic averaging technique.
The arithmetic average will yield the highest average permeability,