Pickett Plot: Log Crossplot for Water Saturation and Rw Determination

What Is a Pickett Plot?

Pickett plot (also called a Pickett crossplot) is a log-derived graphical technique in which the logarithm of true formation resistivity (Rt) is plotted on the vertical axis against the logarithm of porosity on the horizontal axis, allowing simultaneous determination of water saturation (Sw), formation water resistivity (Rw), and the cementation exponent (m) directly from the data without independently knowing Rw in advance. Introduced by G.R. Pickett in 1966, the method exploits the linear relationship predicted by the Archie equation so that water-saturated formation points fall along a straight line whose slope is negative m and whose intercept on the resistivity axis at 100% porosity equals the product of a/Rw, while hydrocarbon-bearing zones appear displaced above and to the left of that line at reduced resistivity for a given porosity.

How the Pickett Plot Works

The theoretical basis of the Pickett plot is the Archie equation: Sw to the power of n equals (a times Rw) divided by (phi to the power of m times Rt). Taking logarithms of both sides and rearranging for the case of 100% water saturation (Sw = 1) gives: log(Rt) = -m times log(phi) plus log(a times Rw). This is a straight line on a log-log plot of Rt versus phi with slope -m and y-intercept log(a times Rw). When a formation water sample or known wet zone is available, the petrophysicist identifies the cluster of clean, water-bearing data points in the interval, fits the line through them, reads the slope to obtain m (typically 1.8-2.2 for sandstones, 2.0-2.5 for carbonates), and reads Rw from the extrapolated intercept. The tortuosity factor a is conventionally assumed to be 1.0 for most applications, though it can be adjusted if core data indicate otherwise.

Once the 100% water saturation line is established, iso-saturation lines for any Sw value are drawn parallel to it, displaced upward on the resistivity axis by the factor Rw divided by (Sw to the power of n times phi to the power of m). For n = 2 (the Archie default saturation exponent), each successive halving of water saturation shifts the parallel line upward by a factor of 4 in resistivity. Pay zones appear as data clusters or individual points plotting above the water line, with points near the 50% Sw line representing the economic cutoff in many reservoir types. The visual separation from the water line gives a rapid qualitative sense of pay quality before any numeric Sw calculation is performed. The analyst scans each logged interval, plots the porosity-resistivity pair, and flags points that rise clearly above the water saturation trend.

Constructing the plot in practice requires clean, shale-free porosity estimates from a density-neutron crossplot or sonic log and deep resistivity readings from an induction or laterolog tool. Intervals with obvious lithology changes, heavy minerals, or pyrite should be excluded because these perturb both porosity and resistivity readings independently of fluid content. Overprinting the plot with depth or formation labels, color-coded by lithology or stratigraphic unit, helps identify systematic offsets between different reservoir units that may indicate different m values, different water salinity zones, or different pore geometries.

Limitations and Comparison to Other Crossplots

The Pickett plot assumes the Archie equation is valid, which requires that the formation is clean (clay-free), that the pore space is intergranular with no significant fracture or vug porosity, and that the connate water salinity is uniform throughout the interval being plotted. In shaly formations, clay minerals contribute their own electrical conductivity (the Waxman-Smits or dual-water effect), which reduces Rt relative to a clean sand at the same Sw and causes data points to fall below the true water saturation line. The result is apparent Sw values higher than the actual value, a bias that can cause petrophysicists to classify producible hydrocarbon zones as wet and fail them. Corrections for clay volume using the Waxman-Smits or Indonesia equation are applied before plotting, or the analyst uses a shale-corrected resistivity.

The Hingle plot is an alternative crossplot that displays the same Archie relationship in a linear rather than log-log format, plotting Rt to the power of 1/n on the vertical axis against porosity raised to the m/n power on the horizontal axis. The Hingle plot has the advantage of making the water saturation lines converge on a single point (the pivot point) rather than being parallel, which some analysts find easier for visual identification of the formation water line. However, the Pickett plot is generally preferred in practice because its log-log scaling spreads the data more evenly across the range of porosity and resistivity values encountered in real wells, and because the slope of the water line directly equals -m without requiring iteration. Both plots require the same input data and share the same Archie equation assumptions, so neither is inherently more accurate; the choice is typically one of analyst preference and software availability.

Pickett Plot Synonyms and Related Terminology

• Pickett crossplot -- the most common alternative name, used interchangeably with Pickett plot in petrophysics literature and software menus
• log-log resistivity-porosity crossplot -- a descriptive label used in technical papers when the author wants to be explicit about the axis scales without implying a specific methodology
• Hingle plot -- a related but distinct crossplot using linear axes with transformed variables; used for the same Sw determination purpose but with different visual properties
• Archie crossplot -- informal term sometimes used when the analyst is emphasizing the direct application of the Archie equation rather than referencing Pickett's specific formulation

Related terms: Archie equation, water saturation, formation water resistivity, cementation exponent, porosity, resistivity log, petrophysics

Frequently Asked Questions About Pickett Plot

Can you build a Pickett plot if you have no known wet zone in the well?

Yes, with caution. If regional data from nearby wells provide a reliable Rw value and an expected cementation exponent for the formation, the analyst can draw the predicted water saturation line and overlay the new well's data to identify pay. Alternatively, if the well is believed to penetrate the aquifer below the hydrocarbon contact but the interval is not definitively identified on logs alone, the analyst can assume the lowest-resistivity, highest-porosity cluster represents wet rock and anchor the line there. This introduces uncertainty and should be documented explicitly in the petrophysical report. A formation water sample or a repeat formation tester (RFT/MDT) water sample is far preferable to assumption-based Rw estimation.

What does it mean when points scatter widely rather than forming a clear trend?

Wide scatter on the Pickett plot typically indicates one or more of the following: significant lithology variation across the plotted interval (mixing carbonates, sandstones, and silts), variable shale content causing independent perturbations to both porosity and resistivity, multiple water salinity zones with different Rw values (especially in mixed fluvial-marine sequences), borehole rugosity affecting pad-tool porosity readings, or invasion of drilling fluid that has altered the near-wellbore resistivity to something other than the true formation value. The analyst should re-examine the gamma ray and lithology logs, subset the data by facies or lithology, and replot each subset separately. A coherent trend emerging within a single lithology subset confirms that the scatter was a mixing effect rather than an intrinsic measurement problem.

How does the Pickett plot handle gas-bearing formations differently from oil-bearing formations?

Gas causes the density-neutron crossover effect, which means the neutron-density average porosity underestimates true porosity in gas zones. If the analyst uses this uncorrected porosity on the Pickett plot, gas-bearing points will appear shifted left (to lower apparent porosity) relative to their true position, making them plot at an even higher displacement above the water line than they should. This is visually dramatic and clearly signals pay, but the Sw value calculated from the apparent porosity will be erroneously low. A gas-corrected or density-only porosity should be used in gas-prone intervals to obtain a reliable Sw estimate from the Pickett plot rather than merely a qualitative pay flag.

Why Pickett Plot Matters in Oil and Gas

The Pickett plot remains one of the most efficient and reliable tools in the petrophysicist's toolkit because it solves simultaneously for variables that would otherwise require independent measurement or regional database lookup. In frontier wells where formation water geochemistry is unknown, the ability to read Rw directly from log data can be the difference between completing a well in a pay zone and bypassing it because water saturation could not be reliably calculated. The visual nature of the crossplot also provides a quality-control check on the Archie equation parameters: if the assumed m value produces a water line slope that clearly does not fit the wet data cluster, the discrepancy is immediately visible and prompts investigation of the rock physics assumptions. For these reasons, industry petrophysical guidelines from the Society of Petrophysicists and Well Log Analysts (SPWLA) and most major operating company workflows require a Pickett plot as part of the standard log analysis package for any new formation evaluation, regardless of whether more sophisticated models such as Waxman-Smits or dual-water are subsequently applied.