Pickett plot

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A Pickett plot is a method used in petrophysical analysis to evaluate formation characteristics of conventional, granular reservoirs. It was developed by professor George Pickett. The method provides a graphical solution to Archie’s equation to determine water saturation of a reservoir by plotting resistivity versus porosity on a log-log scale.[1]

Background

Archie's Equations [2]

Archie’s Equations describe the empirical relationship between the formation factor F, porosity ϕ, water saturation Sw, and resistivities R, in granular rocks.

Archie equation1.png eq. (1)

Archie equation2.png eq. (2)

Where:

a = proportionality constant varying from 0.6 to 1.5

m = cementation factor that varies between 1.3 and 3

n = saturation exponent, often assumed to be 2

Ro = resistivity of the formation when 100% saturated with formation water

Rw = resistivity of the formation water

Rt = true resistivity of the formation

Manipulation of Archie's Equations[3]

Solving for R0 in equation (2) and plugging into equation (1) yields

Archiev2.JPG

Isolate ϕm on the left hand side and take logarithms of both sides of the equation to obtain

Archiev3.JPG

Adapting the equation to the desired form of the plot yields

Archiev4.JPG eq. (3)

Equation (3) describes a set of parallel lines on the Pickett plot that indicate water saturation, Sw.

Construction[1]

Step 1: Plot Reservoir Data Points

Select reservoirs for evaluation from the well log. Plot the points on a 2x4 cycle log-log graph by using the true resistivity, Rt, on the x-axis and porosity, ϕ, on the y-axis.

Step 1. Credit: http://wiki.aapg.org/Pickett_plot_construction

Step 2: Plot Rw

Plot the point for the resistivity of the formation water, Rw. This point should be plotted at 100% porosity since it is accounting for only the resistivity of the water and not the resistivity of the reservoir rock. The value of the resistivity can be obtained from logging reports or calculated from the spontaneous potential.

Step 2. Credit: http://wiki.aapg.org/Pickett_plot_construction

Step 3: Plot 100% Sw Line

As seen in the manipulated Archie’s equation, the slope of the Sw lines comes from the cementation factor, m. If the porosity type is known then m can be obtained from a table of empirical values. If not, then a value of m = 2 for clean sandstone is commonly used. To plot the 100% saturation line begin at the Rw point and draw a line with a slope of -1/m using a linear scale. When there is limited data about porosity type an alternative option is to assume that there are fully saturated water zones in the reservoir and therefore plot the 100% Sw line at the most "southwest" edge of the data points

Step 3. Credit: http://wiki.aapg.org/Pickett_plot_construction

Step 4: Plot Remaining Sw lines

Mark the intercept of the 100% Sw line and Rt = 1. Draw a line from this point towards the right, parallel to the x-axis. Mark where this line passes through the Rt values of 2, 4, 6, 8, 14, and 20. Draw lines through these points parallel to the 100% Sw line. These lines represent Sw percentages of 71, 50, 41, 35, 27, and 22.

Step 4. Credit: http://wiki.aapg.org/Pickett_plot_construction

References

  1. 1.0 1.1 [ Pickett, G., R., 1973, Pattern recognition as a means of formation evaluation: The Log Analyst, vol. 14, no. 4, p. 3–11.]
  2. [ Archie, G. E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics: Petroleum Transactions of AIME 146: 54–62.]
  3. [Krygowski, D. A., & Cluff, R. M. (2013). Pattern Recognition in a Digital Age: A Gameboard Approach to Determining Petrophysical Parameters. Retrieved March 19, 2018, from https://library.seg.org/doi/pdf/10.1190/urtec2013-266]