Page 509 - Petrophysics

MULTIPLE-PERMWILITY ROCKS 477

Figure 7.18. Radialflow through segments in series.

If Equation 7.162 is solved for the average permeability, one can derive
the following general equation (where r, = re and r, = rw):

(7.163)

Equations 7.159 and 7.163 apply to gas as well as oil reservoirs. This
can be demonstrated by using the linear gas flow Equation 7.18 with
Equations 7.147 and 7.155 to derive, respectively, Equations 7.15 1 and
7.159. Equations 7.154 and 7.163 can be derived by using the radial gas
flow Equation 7.103 for f = 1 and s = 0 with Equations 7.147 and 7.155,
respectively.

EXAMPLE

The permeability of a 160-acre light-gas formation drained by a
single well is 15 mD. The well was heavily acidized to a permeability
of 25 mD and a radius of 30 ft, and then completed. During well
completion, a 2-ft thick damaged zone developed in the vicinity of
the wellbore. The permeability of this damaged segment is 4 mD. The
wellbore radius is 0.50ft. Calculate the average permeability of this
drainage area.