Page 282 - Petrophysics 2E

FLOW UNITS FOR SWY SANDSTONES 255

exponent n are constant within a given flow unit. In order to identify flow
units, a permeability-porosity relationship is necessary. This relationship
is then combined with a shale model that best describes the pay zone of
interest, to derive the slope Hsh and intercept FZI,h. If, for instance, the
saturation exponent is equal to 2, the total shale model can simply be
written as:

(4.106)

The Timur permeability-porosity relationship is:

($4.4
k = 85817- (4.107)
sw

The Wyllie and Rose relationship is:

k = 62,500, o6
sw (4.108)

The generalized form of the Timur or Wyllie and Rose permeability-
porosity model is:

(4.109)

where C1 and C2 are correlation constants. In the case of Timur
(Equation 4.103, n = 2, C1 = 8581, and C2 = 4.4, where k is in mD
and porosity and saturation are expressed in fractions. For the Wyltie
and Rose equation (Equation 4.108), n = 2, C1 = 62,500, and C2 = 6,
where k is in mD and @ and S, are fractions.
Assuming the pay zone has low shale content (v,h -= lo%), i.e. csh is
approximately zero, then combining Equations 4.101 , 4.106, and 4.109
and solving for RQI yields:

Log(RQ1) = (

Assuming Wyllie and Rose is applicable and substituting for C1 and CZ
gives:
( E>
Log(RQ1) = (0.5m + 2.5) Logo + Log 78.5 - (4.111)