Pore Pressure

Purpose

Pore pressure is the pressure of the fluid in the rock's pores. It decides the mud weight that can safely be used to drill: a mud weight too low allows a kick, and one too high fractures the formation and loses fluid. Below the depth at which the pressure first departs from hydrostatic it is also an input to the geomechanical model, through the Vertical effective stress that controls the strength of the rock and the stress state. This step estimates pore pressure in shale from the sonic or resistivity log, and keeps it consistent with the overburden and measured pressures.

Position in the workflow

Upstream. The inputs are a clean, depth-matched, repaired sonic and resistivity log from Stage 1, a bulk density log for the overburden (with washouts repaired), and a shale volume curve to select the shale points. Bad hole, cycle skips and hydrocarbon effects in the logs all become pressure errors.

Downstream. The result feeds:

the overpressure curve and the equivalent mud weight used in the mud weight window,
the effective stress used in the vertical and horizontal stress calculation, and in wellbore stability, and
a check of the shear and elastic moduli, since pore pressure and unloading affect the velocities.

Error propagation. Pressure is a difference between two large numbers, the overburden and the effective stress. An error of 0.1 g/cm³ in mean density changes the overburden at 10,000 ft by about 350 psi (0.7 ppg), and an error in the exponent or trend of the same size can add as much. A mud weight window is often only 0.5 to 1 ppg wide, so these errors matter.

Key concepts

Effective stress. Terzaghi effective stress: the vertical effective stress is the overburden less the pore pressure. Rock velocity and resistivity respond to the effective stress, through the porosity, and so can be read backward to give pressure. Normal pressure is the hydrostatic pressure, and overpressure is the excess above it.

Normal compaction trend. A Normal compaction trendline describes how a property changes with depth when pressure is hydrostatic. Methods such as Eaton's and equivalent depth work on the departure from it. See the trendline page.

Mechanisms of overpressure. Disequilibrium compaction keeps the rock on its loading curve with low effective stress. Mechanisms that expand the fluid, such as hydrocarbon generation and clay diagenesis, or that move pressure laterally, cause Unloading: velocity and density stay higher than the loading relation implies. The methods differ in how they handle this. See the loading vs unloading page.

Units. Pressures are in psi and often as an equivalent mud weight, Equivalent mud weight, in ppg: pressure in psi divided by 0.052 times the true vertical depth in feet. Gradients are in psi/ft. Velocity methods are written in ft/s and psi.

Shale only. The log relations apply to clay-rich shale. Sand and carbonate intervals have to be nulled or filled with hydrostatic pressure and the pressure in a sand is set by measurements or by centroid transfer from the adjoining shale, not by a log trend.

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
Eaton	Sonic or resistivity; trendline; overburden; hydrostatic; exponent	A trendline can be fitted and the overpressure comes from compaction disequilibrium	Simple, fast, widely used; sonic and resistivity forms	Exponent must be calibrated; does not handle unloading; relies on the trend
Bowers	Sonic velocity; overburden; V0, A, B; optionally U and Vmax	Unloading mechanisms are suspected, or a stress-velocity calibration can be made	Works in effective stress; has an unloading curve	Needs more calibration; the onset of unloading is judgmental
Equivalent depth	Log; trendline; overburden profile	A quick consistency check, or when no exponent can be calibrated	No empirical exponent	Assumes loading; sensitive to the trend; weak at shallow depth
Overburden and hydrostatic	Density log; extrapolation; water gradient	Always: they are inputs to every method	Defines the normal case and the limit	Errors in density carry directly into pressure
Normal compaction trendlines	Shale-filtered sonic or resistivity	Before Eaton and equivalent depth	A single trend is easily checked	Biased if fitted in overpressure; one trend per compaction province
Loading vs unloading	Velocity, density, geology	To decide which curve applies	Explains differences between methods	The diagnosis needs data outside the sonic log

Decision guidance

Start with the overburden, hydrostatic pressure and a trendline: every method needs them.
If the overpressure is by rapid burial and measurements support it, Eaton's method with calibrated exponents is the default.
If the shale is in a thermal or gas-generation window, or velocity stops increasing with depth while density does, test Bowers' method with the unloading curve.
Use the equivalent depth method as a cross-check of the Eaton result; if they differ widely the trend is the first suspect.
If there is no calibration data, give the loading and unloading results as a range.

Shared parameter picking

Overburden and hydrostatic. One overburden curve and one water gradient, built once (see the overburden page) and used by every method, so that the methods differ only in how they estimate effective stress.

Shale filter. One shale flag, from Shale volume or Clay volume above a cutoff such as 0.5 to 0.7 (the value is a judgment for the basin), is applied to all curves. Intervals outside the flag are nulled, or set to hydrostatic.

Normal compaction trendlines. The sonic and resistivity trends are shared by Eaton and equivalent depth; Bowers' method replaces them with a virgin curve in effective stress.

Calibration to measured pressure. Formation tester pressures in sands, mud weights, kicks and losses are the data against which every exponent and curve parameter is tuned. Use the same data for each method.

Units and datum. True vertical depth from one datum, pressures in psi (or ppg through the 0.052 factor), velocity in ft/s where Bowers is used.

Recommended default approach

Absent other information, a careful generalist would:

Repair the density log and build the overburden and the hydrostatic pressure, with the water gradient of the basin.
Flag the shale intervals and fit sonic and resistivity trendlines in the normally pressured shale, excluding washouts.
Compute Eaton's pressure with the standard exponents (3 for sonic and 1.2 for resistivity) as a first pass.
Compare with all measured pressures and mud weights, and adjust the exponents to match them. Do not adjust the trend to fit a few points.
Compute the equivalent depth result as a cross-check, and Bowers' result with loading and, if the geology supports it, unloading curves, and report the range.
Report the final curve as pressure in psi and as equivalent mud weight, with the overburden and hydrostatic curves for reference.

Combining methods

The methods use different assumptions, and their disagreement is informative. Averaging them is not a good idea: if one method is wrong because of unloading, an average only dilutes the error. Instead choose a main method by calibration (the one which reproduces measured pressures) and show the others as bounds. The sonic and resistivity versions of Eaton's method are alternatives for the same shale, and where both are good their agreement supports the trend. Where they differ, check the resistivity temperature correction and hydrocarbon effects first. A common practical presentation is a loading result as a lower bound and an unloading result as an upper bound, with the measured pressures overlaid.

QC of results

A good result:

is hydrostatic (or within measurement error of it) in the normally pressured interval used to fit the trend,
is between hydrostatic and the overburden, and rises smoothly in thick shale,
matches formation tester pressures, mud weights and kick and loss data, and
is not computed in sand, coal or carbonate.

Signs of a bad result: pressure that follows lithology changes between sand and shale, pressure that drops below hydrostatic without a reason, a result that exceeds the overburden, and a systematic offset from every measured point.

Common pitfalls

Fitting the trend in an interval that is already overpressured.
Using sand or carbonate points in the trend, or applying the method in them.
Carrying the standard exponents to a new basin without calibration.
Using an overburden from an unrepaired density log, or an extrapolation that is too dense, above the log.
Applying a loading method (Eaton, equivalent depth) where fluid expansion has unloaded the rock, and underestimating the pressure.
Mixing units: slowness in µs/ft with velocity in ft/s, psi with ppg, measured with true vertical depth.
Treating the result as a measurement: it is a model, and measured pressures take precedence.
Using a resistivity that is not corrected for temperature, or that reads hydrocarbons.

Going Deeper

Log-based pore pressure prediction began in the 1960s with trendline methods based on shale resistivity and sonic slowness, followed by Eaton's empirical equations in the early 1970s, and by effective stress methods in the 1990s that separate loading from unloading. More recent work includes basin modeling and seismic velocity inversion for pressure ahead of the bit, and methods that explicitly use the Biot coefficient and the horizontal stress. The persistent difficulty is that velocity, resistivity and density all respond to effective stress and to other things at once: lithology, temperature, cement and fluids. Every method therefore relies on calibration to measured pressures, and the best result usually comes from agreement between more than one method and the direct data.