The Pickett Plot

Part 7, Chapter 7: Archie's Equation and Water Saturation

Learning objectives

Plot porosity against true resistivity on log-log axes
Recognize each Sw as a parallel line of slope -1/m
Read Rw and m from the 100 percent water line
Read a point's Sw from the family of lines

Archie on Log-Log Paper

The Pickett plot is Archie's equation drawn out. Take logs of $R_t = a,R_w/(\phi^{m},S_w^{n})$ and the porosity becomes a straight line in the resistivity:

\log\phi = \tfrac{1}{m}\big(\log(a\,R_w) - \log R_t\big) - \tfrac{n}{m}\log S_w.

On a plot of porosity (up) against true resistivity (right), every water saturation is a line, and because only the last term changes with $S_w$ , the lines are all parallel, each with slope $-1/m$ .

The Wet Line

The most useful line is $S_w = 100%$ , the wet line along the lower-left edge, because it is fixed by the rock alone. Its slope is $-1/m$ , so it reads the cementation exponent straight off the chart, and its position is set by $R_w$ , so it reads the water resistivity too, both without assuming either in advance. That is why a Pickett plot is the first thing an analyst draws: it calibrates $m$ and $R_w$ from the wet points before any saturation is computed.

Reading Sw, and a Warning

With the family drawn, any point reads its water saturation by eye, by which lines it falls between, and a point above and to the right of the wet line holds hydrocarbon. There is a bonus: a real cloud of points that does not fall on a clean set of parallel lines is a warning that the simple Archie model is wrong for the rock, a shaly sand, perhaps, or a complex carbonate. The Pickett plot is as much a quality check as a calculator.

References

Pickett, G. R. (1973). Pattern recognition as a means of formation evaluation. The Log Analyst, 14(4).
Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.