American Oil and Gas Reporter - November 2015 - 88

SpecialReport: MWD/LWD Technology
FIGURE 2B
Pickett Plot with BVW Lines at Data Point Locations
a*Rw
1.0

Increasing BVW

BVWirr
Sw=1.0

Sw=0.8
Sw=0.6
Sw=0.4
Sw=0.2
BVW=0.05
BVW=0.07
BVW=0.1

0.1

eas
ing

Slope = -1/cementation exponent, m

BVW=0.15
BVWirr=0.04

De
cr

Porosity

Slope = (m-n)

Data
Sw=1.0
0.01
0.01

0.1

100

1,000

Resistivity

The porosity-water saturation product
is the bulk volume water fraction of the
porosity, or bulk volume water (BVW).
Figure 1 shows Buckles plots in two
forms: a plot with linear scales (left) and
a plot with logarithmic scales (right). In
the linear plot, the equal BVW values
are hyperbolas, while in the full logarithmic plot, the iso-BVW lines are linear.
The displays provide the same information;
the choice of which to use is up to the interpreter. For intervals at irreducible water
saturation (Swirr) and with a range of
porosities, the bulk volume water is irreducible (BVWirr).
A Pickett plot is a graphical solution
to Archie's equation. As shown in Figure
2A, the plot is full logarithmic. That is,
both scales are logarithmic, with resistivity
on the x-axis and porosity on the y-axis.
From the location of the points, a waterbearing line can be drawn at the southwestern edge of the data. From that line,
assuming a value for the saturation exponent (n), a family of lines of decreasing
water saturation can be drawn parallel to
the water-bearing line.
The water saturation of each point
can be read directly from the plot. The
numeric calculation of Archie's equation
is bypassed, as is the need to input formation water resistivity (Rw) data. In
addition, two parameters in Archie's
equation are predicted by the plot: the
porosity exponent (m) from the negative
inverse of the slope of the water-bearing
line, and Rw from the intercept of the
water-bearing line at a porosity equal to
88 THE AMERICAN OIL & GAS REPORTER

1.0 (100 percent), with a user estimate of
the Archie equation factor (a).

Bulk Volume Water
Figure 2B shows bulk volume water
lines added to the Pickett plot. If there is
a sufficient range of porosity at irreducible
water saturation, the slope of the BVWirr
line can be determined. The saturation
exponent, n, can be estimated by determining m from the slope of the waterbearing line, and the slope of the BVW

lines. If n is equal to m, the BVW lines
will be vertical.
Zones at the lowest value of BVW
(eastern edge of the data) are at BVWirr
and should produce only hydrocarbons.
Conversely, the points at the southwestern
edge of the data are in the water-bearing
zone, and will produce only water. The
points between those two edges are in
the transition zone, where some combination of water and hydrocarbons will
be produced.
A Hingle plot is used to determine
water saturation from resistivity and
porosity. The x-axis in the right-hand
plot in Figure 3 shows porosity increasing
from zero to 100 percent moving toward
the right. Instead of using a calculated
porosity, raw bulk density or acoustic
slowness can be used.
The y-axis is a nonlinear scale, shown
in the figure in both resistivity and conductivity. In use, data points are plotted
by porosity and resistivity. From the location of the points, a water-bearing line
again can be drawn at the northwestern
edge of the data, with a family of lines of
decreasing water saturation fanning out
from the intercept of the water-bearing
line at the x-axis.
The Sw of each point can be read directly from the plot. If bulk density or
acoustic slowness are plotted instead of
porosity, the x-intercept of the waterbearing line predicts the matrix value.

FIGURE 3
Sw Values from Hingle Plots

American Oil and Gas Reporter - November 2015

Table of Contents for the Digital Edition of American Oil and Gas Reporter - November 2015