Formation Evaluation Through Casing - Cased-Hole Log Analysis and Reservoir Performance Monitoring - page 178

adds one more for a total of four measurements. Therefore, one unknown must be
eliminated before a solution can be found. The normal way of doing this is to make
an assumption about V wb as a function of V dc . That is, to assume that a unit volume
of dry clay always has associated with it the same amount of bound water. In fact,
in “pure shale,” it would be quite common to find a “total porosity” of 30 or 40 %
(as reflected by neutron log readings in shales). In this case, the amount of bound
water associated with a dry clay can be back calculated.
For example, if a 100 % shale has a total porosity of 35 %, it follows that:

V = 35 % and V = 65 %

wb dc

and hence that:

=a .

V V ,

wb dc

where ʱ is some constant which, in this example, is numerically equal to
35/65 = 0.538. Having reduced the unknowns to four ( V ma , V dc , V wf , and V hy ), since
V wb can now be assumed equal to ʱ · V dc , the solution to the dual-water problem
becomes straightforward.
The following steps are required:

1. Find all necessary parameters ʣ ma , ʣ dc , ʣ wf , ʣ hy , GR ma , GR dc .
2. Find ˕ T and V dc .
3. Solve for ˕ e and S we .

Finding Parameters

Crossplot techniques are particularly useful for finding the required parameters. The
log data points should be divided into two groups: The 100 % shales and the clean-
formation intervals. In clean formations, a plot of ʣ vs. ˕ will deine ʣ ma and ʣ wf ,
provided there is sufficient variation in porosity and enough points at 100 % water
saturation. Figure 11.37 shows the procedure schematically.
A similar plot for inding ʣ dc and ʣ wb is shown in Fig. 11.38 (all points must come
from the shale sections). Note that, on both plots, ˕ T , derived from the ʣ vs. ratio
crossplot, is used. This entails an assumption that porosity measured in this way is,
in fact, equal to total porosity.