Page 104 - Well Logging and Formation Evaluation

94 Well Logging and Formation Evaluation

The S measured by the tool is assumed to be a linear sum of the volume
fractions of the components times their respective S values. Clearly the
accuracy of the tool in differentiating oil and water is dependent mainly
on the contrast in S between the oil and water. Hence the tool works well
in saline environments and poorly in fresh environments. Even in a saline
environment it might be found that small changes in the input parameters
result in a large change in S w. Hence the tool can give very unreliable
results unless some of the water saturations are already well known in the
formation.
The tool also has a limited depth of investigation, sufficient to pene-
trate one string of casing but not always two. It is essential to have a
completion diagram of the well available when interpreting the tool, so
that the relevant positions of tubing tail, casing shoes, and tops of liners
are known.
Where the tool is used in time-lapse mode in a two-fluid system, clearly
the variables relating to the nonmovable fluids drop out and changes
in S w can be calculated on the basis of only (S w -S hydrocarbon). Some of
the equations that may be used for interpreting the tool will now be
derived:

Two-component system without time-lapse mode:

- - ) f * S + V sh * + f* S w * S + f* (1 - S w * (5.7.1)
)
S = (1 V sh m S shale w S h
where V sh denotes the total volume fraction of shale. From which:

)
-
)
S w = ( [ SS m - f* (S h - S m - V sh * (S sh - S m [f* (S w - S h )] (5.7.2)
)
Two-component system in time-lapse mode:
S 2 - S 1 = (S w 2 - S w * S - S )*f (5.7.3)
) (
1
h
w
From which:
S w2 = S w1 + (S 2 - S 1 [ w - S *f ] (5.7.4)
) (S
)
h
For a situation in which gas replaces oil with constant water satura-
tion in time-lapse mode:

S 2 - S 1 = S g * ( S - S )*f (5.7.5)
o
g