Page 552 - Petrophysics

PETROPHYSICAL PROPERTIES 519

and Darcy's law is:

AP
q=kA- (8.3 1 b)
PL

Equating these two equations and solving for permeability results in:

(8.32)

The physical difficulty in using equation 8.32 is that the number of
fractures, fracture height, and fracture width have to be known. Since,
by definition,

(8.33)

and

(8.34)

substituting Equation 8.34 in 8.32 yields:

(8.35)

Equation 8.35 is similar to Equation 3.14, k = @r2/8, where the capillary
radius r and constant 8 have been replaced by the fracture width wf and
12 respectively. Equation 8.35 is commonly used to calculate fracture
permeability. Expressing fracture porosity in percent and fracture width
in micrometers (pm), Equation 8.38 becomes:

where kf is expressed in darcies.
Equation 8.35 can be used to calculate wf if the porosity and
permeability are known from well logs or well testing:

k
Wf = 42- (8.37)
@