Overview
Formation (pore) pressure prediction is essential for safe drilling, mud weight selection, and well planning. The Eaton method (1975) is the most widely used technique for estimating pore pressure from well logs (sonic, resistivity, or d-exponent). It compares observed log values to a normal compaction trend and quantifies the overpressure based on the deviation.
Theory
In normally pressured formations, compaction increases monotonically with depth, causing porosity to decrease and velocity/resistivity to increase along a predictable trend (Normal Compaction Trend Line, NCTL). When formation pressure exceeds normal hydrostatic (overpressure), the rock is under-compacted for its depth, causing the log response to deviate from the NCTL.
Eaton's method quantifies this deviation using empirical exponents calibrated to specific basins.
Formulas
Eaton's Method — Sonic Log
Pp = OBP - (OBP - Pn) * (Δt_n / Δt_obs)^3.0
| Symbol | Description | Units |
|---|---|---|
| Pp | Pore pressure | psi |
| OBP | Overburden pressure | psi |
| Pn | Normal hydrostatic pressure | psi |
| Δt_n | Normal compaction transit time at depth | μs/ft |
| Δt_obs | Observed transit time | μs/ft |
Eaton's Method — Resistivity Log
Pp = OBP - (OBP - Pn) * (R_obs / R_n)^1.2
where R_obs = observed resistivity, R_n = normal resistivity at that depth.
Eaton's Method — d-Exponent
Pp = OBP - (OBP - Pn) * (dc_obs / dc_n)^1.2
where dc = corrected d-exponent.
D-Exponent (Jorden & Shirley, 1966)
d = log(ROP / (60*RPM)) / log(12*WOB / (1000*Dbit))
Corrected d-exponent:
dc = d * (MW_normal / MW_actual)
Overburden Pressure
OBP = ∫ ρ(z) * g * dz
In practice:
OBP_gradient ≈ 1.0 psi/ft (onshore) or calculated from density log
OBP = Σ (0.052 * ρ_bulk_i * Δz_i)
Normal Pore Pressure
Pn = 0.433 * TVD (psi) [freshwater gradient]
Pn = 0.465 * TVD (psi) [Gulf of Mexico saltwater]
Worked Example
Given: TVD = 12,000 ft, OBP gradient = 1.0 psi/ft, normal Δt at 12,000 ft = 85 μs/ft (from NCTL), observed Δt = 110 μs/ft.
Step 1: Overburden pressure:
OBP = 1.0 * 12,000 = 12,000 psi
Step 2: Normal pore pressure (Gulf of Mexico):
Pn = 0.465 * 12,000 = 5,580 psi
Step 3: Eaton pore pressure (sonic):
Pp = 12,000 - (12,000 - 5,580) * (85/110)^3.0
= 12,000 - 6,420 * (0.7727)^3
= 12,000 - 6,420 * 0.4613
= 12,000 - 2,961
= 9,039 psi
Step 4: Equivalent mud weight:
EMW = 9,039 / (0.052 * 12,000) = 14.49 ppg
This is significantly overpressured (normal = 8.94 ppg).
Valid Ranges
| Parameter | Typical Range |
|---|---|
| Eaton sonic exponent | 3.0 (standard; 1.0–5.0 basin-dependent) |
| Eaton resistivity exponent | 1.2 (standard; 0.6–1.5) |
| Normal pore pressure gradient | 0.433 – 0.465 psi/ft |
| OBP gradient | 0.8 – 1.1 psi/ft |
| Overpressure onset | Typically 5,000 – 15,000 ft |
Limitations
- Requires a well-defined Normal Compaction Trend Line
- Exponents are basin-specific — must calibrate with offset well data
- Does not work in carbonates (non-compaction related overpressure)
- Unloading (aquifer charging, lateral transfer) cannot be detected by compaction methods
- Sonic Δt affected by gas, lithology, and borehole conditions
- Eaton, B.A. (1975). "The Equation for Geopressure Prediction from Well Logs." SPE-5544.
- Hottman, C.E. & Johnson, R.K. (1965). "Estimation of Formation Pressures from Log-Derived Shale Properties." JPT, 17(6), 717–722.
- Jorden, J.R. & Shirley, O.J. (1966). "Application of Drilling Performance Data to Overpressure Detection." JPT, 18(11), 1387–1394.
- PetroWiki — Pore pressure: https://petrowiki.spe.org/Pore_pressure