Page 95 - Introduction to Petroleum Engineering

DIRECTIONAL PERMEABILITY 79
4.4 DIRECTIONal PERMEabIlITY

In general, the value of permeability depends on direction. The directional dependence
of permeability is often represented in the {x, y, z} directions as {k , k , k }.
y
x
z
Permeability in a porous medium is considered isotropic if permeability does not
depend on direction so that k = k = , otherwise permeability is considered
k
x
z
y
anisotropic.
In many reservoirs, permeability in the horizontal plane (k = k ) is about 10
x
y
times the permeability in the vertical direction k . This difference is usually more
z
pronounced in sandstones than in limestones, and it results from layering that is
visible in sandstones. Permeability parallel to the direction of deposition of the
layers is greater than permeability perpendicular to the direction of deposition of
the layers. In many sandstone reservoirs, the layers are horizontal or nearly so.
But in other sandstone reservoirs, the layers are inclined. Layer inclination
depends on the local depositional environment and geological events such as
folding and tectonic activity.
A medium is considered homogeneous if permeability is isotropic at a point
in the medium and the directional values of permeability do not change from
one position in the medium to another. If permeability varies from one point in
the medium to another, the medium is considered heterogeneous. Virtually all
reservoirs exhibit some degree of anisotropy and heterogeneity, but the flow
behavior in many reservoirs can be approximated as homogeneous and
isotropic.
The effect of the directional dependence of permeability on fluid flow is illus-
trated in Figure 4.6 (see also Fanchi, 2010). Part A is a sketch of the drainage area of
four production wells with isotropic permeability, and Part B is a sketch of the drain-
age area of four production wells with anisotropic permeability. Fluid flow into the
wells is radial in Part A, while it is elliptical in Part B with flow greater in the direction
of larger directional permeability.

(a) Isotropic (k = k ) (b) Anisotropic (k x k )
y
y
x

FIguRE 4.6 Illustration of the effect of permeability dependence on direction (after
Fanchi, 2010).