A brief introduction for obtaining Rw with the help of Picket Plot used in the Petrophysical Interpretation.

1. Pickett Plot

2. Pickett plot
• The Pickett plot is a visual representation of the Archie equation
• The Pickett method is on the observation that true resistivity (Rt) is a function of porosity, Water
saturation(Sw) and cementation exponent (m).
• The plot is named after G.R. Pickett.
• The plot is based on taking the logarithm of the Archie equation.
𝑅𝑡 =
𝑎 × 𝑅 𝑤
∅ 𝑚 × 𝑆 𝑤
𝑛
• Taking the logarithm of the equation produces:
log 𝑅𝑡 = log(𝑎 × 𝑅 𝑤)-mlog(∅) − 𝑛𝑙𝑜𝑔(𝑆 𝑤)
• If the zone is water bearing 𝑆 𝑤= 1, log 𝑆 𝑤 = 0 𝑎𝑛𝑑 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑟𝑒𝑑𝑢𝑐𝑒𝑠 𝑡𝑜
Log(𝑅𝑡) = log 𝑎 × 𝑅 𝑤 − 𝑚𝑙𝑜𝑔(∅)
• In practice (𝑅𝑡) is usually plotted on the x-axis and the porosity on the y-axis.
• This technique estimates water saturation and can also help determine
• Formation water Resistivity (𝑅 𝑤)
• Matrix parameter for sonic and density logs (∆𝑡 𝑚𝑎 & 𝜌 𝑚𝑎)

3. 𝑅 𝑤 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑝𝑖𝑐𝑘𝑒𝑡𝑡 𝑝𝑙𝑜𝑡
• Formation Water Resistivity (𝑅 𝑤) can be determined from the following equation :
𝑹 𝒘 =
𝑹 𝒐 × ∅ 𝒎
𝒂
• The following equation is derived by using Archie’s Equation as below:
𝑆 𝑤
𝑛
=
𝑎 × 𝑅 𝑤
𝑅𝑡 × ∅ 𝑚
• Rearranging the above equation
𝑎
𝑅𝑡
=
𝑆 𝑤
𝑛
𝑅 𝑤
× ∅ 𝑚
• When 𝑆 𝑤 = 1 𝑠𝑜 𝑅𝑡 = 𝑅 𝑜 and thus the equation would become
𝑎
𝑅 𝑜
=
1
𝑅 𝑤
× ∅ 𝑚
• After Rearranging
𝑅 𝑤 =
𝑅 𝑜 × ∅ 𝑚
𝑎

4. Example 𝑅 𝑤 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑝𝑖𝑐𝑘𝑒𝑡𝑡 𝑝𝑙𝑜𝑡
• Density porosity is plotted on the y-axis and True
Resistivity is on x-axis.
• The water-bearing line (𝑠 𝑤 = 100%) was drawn through
the cluster of points with a slope of -1/2 (m=2)
• The intercept of water bearing line at 100% porosity
(DPHI=1.0) is a × 𝑅 𝑤 and can be determined from 𝑅 𝑜
𝑅 𝑤 =
𝑅 𝑜 × ∅ 𝑚
𝑎
• For some porosity value, read the value of 𝑅 𝑜 from the
water-bearing line on the crossplot. In this case, for a
porosity of 10% (DPHI = 0.10), 𝑅 𝑜 = 4.6 ohm-m.
• Assume a value of tortuosity factor (a). In this case, a =
1.0.
• The value of cementation exponent (m) is determined
from the crossplot. In this case, m = 2.0.
• By substitution in the above equation
𝑹 𝒘 =
4.6 × 0.102.0
1.0
• 𝑹 𝒘 = 0.046 ohm-m at formation temperature

5. Construction of Pickett Plot
• Picket plot can be constructed if we have a value of Rw & m.
• The procedure for making a Pickett plot consists of five steps, detailed below.
1. Plot points of matching porosity and true resistivity (Rt ) on log-log paper.
2. Plot Rw point on the Rt scale.
3. Determine m using the table of values.
4. Plot the 100% Sw line.
5. Plot the lines representing lower values of Sw .
• These points are explained one by one for better understanding.

6. Construction of Pickett Plot
Step 01:Plot points
• Plot points of matching porosity and true
resistivity (Rt) values.
• Use the x-axis for the resistivity (Rt) scale and
the y-axis for the porosity (Φ) scale.

7. Construction of Pickett Plot
Step 02: Plot Rw Point
• Plot the Rw value (resistivity of formation water)
by plotting the Rw point along the Rt scale on the
x-axis at the top of the graph grid where
porosity is 100%.

8. Construction of Pickett Plot
Step 03:Determine m
• Estimate m (cementation factor) using the table
below.
Porosity Type Value of m
Sandstones with diagenetic or detrital clay in pores 1.7-1.8
Formations with clean, macro- to micro-sized pore
throat
2
Formations with vuggy porosity 2.2-3.0

9. Construction of Pickett Plot
Step 04:Plot the 100% Sw line
• On a pickett plot,the value of m determines the
slope of the S
• The first Sw line plotted on a Pickett plot is the
100% Sw line.
• To plot this line, draw a line with a negative
slope equal to m that begins at the Rw point.
• Use a linear scale to measure the slope; for
example, go down 1 in. and over 2 in.

10. Construction of Pickett Plot
Step 05:Plot sw lines
• After plotting the 100% Sw line, plot the lines
representing lower percentages of Sw using this
procedure:
• Find the intercept of Rt = 1 and the 100% Sw line
(made in the last procedure).
• From this intercept, draw a line parallel to the x-
axis across the plot. Any point on this line has
the same porosity.
• Where this line passes through Rt of 2, 4, 6, 8,
14, and 20, draw a series of lines parallel to the
100% Sw line.
• Points on these lines correspond to Sw of 71, 50,
41, 35, 27, and 22%. These percentages are
calculated from the Archie equation using m = 2
and n = 2 at Rt of 2, 4, 6, 8, 14, and 20.

11. Advantages of Pickett Plot
• Water saturation can be predicted without prior knowledge of Rw, a, or m.
• Rw is directly predicted (if tortuosity factor (a) is known or estimated) from the intercept of the water
bearingline at a porosity of 1 (porosity = 100%)
• The advantage of Picket Plot is that similar water saturation values will plot a straight line even if the
porosity and resistivity values vary.
• This allows one to easily separate the formation into zones based on their calculated water saturation or in
gas saturation
• Picket Plot is better because it is good for low porosity formation where small variation of m cause large
variations in Sw.

12. Limitations of Pickett Plot
• One of the weaknesses of the Pickett plot is its inability to handle shaly formation
• Values for pma and ∆tma must be assumed (although in cases with a wide range of porosities in the water
bearing zone.
• A wide range of porosity must be present to positively determine a water-bearing line.
• Formation lithology and water resistivity must be constant over the intervals compared in the plot.

13. Distinguish between Pay zone & Water Leg
• The Pickett plot can be illustrated with the
hypothetical data set of resistivity and porosity
values logged, with “Archie rock” properties and
a simple reservoir profile
• The example consists of a pay section at
irreducible water saturation (zones A-E), a
transition zone (Zone F), above a water leg (zones
G-J).

14. Distinguish between Pay zone & Water Leg
• Zones A to E have much higher resistivities
than zones H to J, even though they have
similar porosities, and suggests that these
zones may have appreciable hydrocarbon
content.
• Zone F is intermediate between these two
clusters, and its depth relationship to them
indicates that it may be in a transition zone.
• The zone H-J trend of a systematic decline in
resistivity with porosity also favors their
interpretation as possible water zones.

15. References
• Basic Well Log Analysis (2nd Edition) By George Asquith & Daniel Krygowski
• http://wiki.aapg.org/Pickett_plot_construction
• http://www.glossary.oilfield.slb.com/Terms/p/pickett_plot.aspx
• http://www.kgs.ku.edu/software/PfEFFER-java/HELP/PfEFFER/Pfeffer-theory3.html