Page 101 - Well Logging and Formation Evaluation

Advanced Log Interpretation Techniques 91

Figure 5.6.2 Thomas-Stieber Plot for Discriminating Dispersed/Laminated Shale

PHIT = (1 V lam * f - (1 f sh * )+ V lam *f sh
-
-
) ( csa
) V dis
where V dis is the volume fraction of dispersed shale in the sand laminae,
and V lam is the volume fraction of laminated shale. This should lead to a
plot as shown in Figure 5.6.3.
Above we have two equations in two unknowns (V lam , V dis ), which can be
solved provided that GR sa , GR sh , f csa , and f sh are all known or can be picked
from the crossplot. The sand porosity f sa may then be determined using:

f sa = f csa - (1 - f sh )* V dis .

V dis may be shown to equal

[ 1- ( [ GR sh - GR 0 (GR sh - GR sa )] ( 1- V lam * - GR sa ) GR sh .
)) (GR sh
In terms of known variables, f sa is given by:

B (
f sa = [ * - f sh ) - * - f sh )] ( [ 1- f sh ) - * f csa - f sh )]
A (1
B (PHIT
where A = (GR sh - GR)/(GR sh - GR sa ) and B = GR sh /(GR sh - Gr sa ).