# Difference between revisions of "Pickett plot"

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==Background== | ==Background== | ||

− | === Archie's | + | === Archie's Equations <ref>[ Archie, G. E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics: Petroleum Transactions of AIME 146: 54–62.]</ref> === |

− | Archie’s | + | Archie’s Equations describe the empirical relationship between the formation factor ''F'', porosity ''ϕ'', water saturation ''S<sub>w</sub>'', and resistivities ''R,'' in granular rocks. |

− | [[File:Archie equation1.png]] | + | [[File:Archie equation1.png]] ''(1)'' |

− | [[File:Archie equation2.png]] | + | [[File:Archie equation2.png]] ''(2)'' |

Where: | Where: | ||

Line 27: | Line 27: | ||

''R<sub>t</sub>'' = true resistivity of the formation | ''R<sub>t</sub>'' = true resistivity of the formation | ||

+ | |||

+ | === Manipulation of Archie's Equations to Describe Water Saturation === | ||

+ | Solving for ''R<sub>0</sub>'' in equation ''(2)'' and plugging into equation ''(1)'' yields | ||

+ | |||

+ | [[File:Archiev2.JPG|114x114px]] | ||

+ | |||

+ | Isolate ''ϕ<sup>m</sup>'' on the left hand side and take logarithms of both sides of the equation to obtain | ||

+ | |||

+ | [[File:Archiev3.JPG|386x386px]] | ||

+ | |||

+ | Adapting the equation to the desired form of the plot yields | ||

+ | |||

+ | [[File:Archiev4.JPG|394x394px]] ''(3)'' | ||

+ | |||

+ | Equation ''(3)'' describes a set of parallel lines on the Pickett plot that indicate water saturation, ''S<sub>w</sub>.'' | ||

==Construction== | ==Construction== |

## Revision as of 13:29, 19 March 2018

**This page is incomplete and is currently being authored by a student at the University of Houston.**

**This page will be complete by March 20, 2018.**

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]}

## Contents

## Background

### Archie's Equations ^{[2]}

Archie’s Equations describe the empirical relationship between the formation factor *F*, porosity *ϕ*, water saturation *S _{w}*, and resistivities

*R,*in granular rocks.

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

*R _{o}* = resistivity of the formation when 100% saturated with formation water

*R _{w}* = resistivity of the formation water

*R _{t}* = true resistivity of the formation

### Manipulation of Archie's Equations to Describe Water Saturation

Solving for *R _{0}* in equation

*(2)*and plugging into equation

*(1)*yields

Isolate *ϕ ^{m}* on the left hand side and take logarithms of both sides of the equation to obtain

Adapting the equation to the desired form of the plot yields

Equation *(3)* describes a set of parallel lines on the Pickett plot that indicate water saturation, *S _{w}.*

## Construction

### 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, *R _{t}*, on the x-axis and porosity,

*ϕ*, on the y-axis.

### Step 2: Plot *R*_{w}

_{w}

Plot the point for the resistivity of the formation water, *R _{w}*. 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 3: Plot 100% *S*_{w} Line

_{w}

As seen in the manipulated Archie’s equation, the slope of the *S _{w}* 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

*R*point and draw a line with a slope of -1/

_{w}*m*using a linear scale.

### Step 4: Plot Remaining *S*_{w} lines

_{w}

Mark the intercept of the 100% *S _{w}* line and

*R*= 1. Draw a line from this point towards the right, parallel to the x-axis. Mark where this line passes through the

_{t}*R*values of 2, 4, 6, 8, 14, and 20. Draw lines through these points parallel to the 100%

_{t}*S*line. These lines represent

_{w}*S*percentages of 71, 50, 41, 35, 27, and 22.

_{w}## References