Page 100 - Well Logging and Formation Evaluation

90 Well Logging and Formation Evaluation

the shale and quartz have a similar matrix density and that the formation
is water bearing.

Laminae:

)
f d = V lam * f sh + (1 - V lam * f csa

f n = V lam ( * HI sh + f sh *HI w )+ (1 - V lam * f csa *HI w
)
where V lam is the volume fraction of laminated shale.

Dispersed:

sh (
-
f d = f csa V *1 - f sh )
f n = HI sh V + HI* sh w * f d

where V sh is the volume fraction of shale.

Structural:

f d = f csa V * f sh
+
sh
f n = f csa *HI w + V sh * f sh *HI w + V sh *HI sh

This is displayed graphically on a f d / f n crossplot in Figure 5.6.2.
Depending on the nature of the shale, the behavior can be seen to follow
different trends. Therefore, if such a plot is made over a section of for-
mation, and the 100% shale and sand points are identified, it may be pos-
sible to differentiate the type of shale fill that is occurring. Note that since
oil and water have a similar HI, a similar behavior would be observed in
an oil reservoir. A greater deviation would be observed in a gas reservoir
since the HI for gas is much less than that for water.
Thomas and Stieber’s method can be extended to other logs besides the
density and neutron. For instance, a similar behavior would be expected
if the total porosity (PHIT) from the density (f d) were plotted against
compressional velocity (V p) or GR. For a PHIT/GR approach, assuming
also that the sand laminae may contain dispersed shale but that structural
shale is not present, the relevant equations are:

) (
-
GR = (1 V lam * GR sand + V dis * GR shale ) + V lam * GR shale