geomechanics · compaction
Compaction-Based Pore Pressure (Equivalent Depth Method)
z* = (1/c)·ln(φ0/φobs); Pp = OBG·TVD − (OBG−Pn)·z*
click formula to derive ↑
Inputs
fraction
fraction
1/ft
psi/ft
psi/ft
ft
Description
Estimates pore pressure from a porosity/density log using Magara's (1978) equivalent depth method: if an undercompacted shale shows the same porosity as a normally-compacted shale at a shallower depth, Athy's (1930) exponential compaction law implies both carry the same effective stress, regardless of burial history. This is the porosity/density-log counterpart to the Eaton Pore Pressure calc's sonic-log method — methodologically distinct, useful as an independent cross-check on the same well.
Variables
| Symbol | Unit | Description |
|---|---|---|
| z* | ft | Equivalent Depth |
| Pp | psi | Pore Pressure |
| EMW | lb/gal | Equivalent Mud Weight |
| φobs | fraction | Porosity observed at the depth of interest, from a density/neutron log or core — typically measured in shale for compaction-disequilibrium analysis. |
| φ0 | fraction | Porosity of the sediment at the time of deposition, before any compaction — typically 0.4-0.7 for shale depending on clay mineralogy, around 0.4-0.45 for clean sand. |
| c | 1/ft | Athy/Magara-type exponential compaction decay coefficient. Published values vary by orders of magnitude across basins and lithologies — treat the default as illustrative only and calibrate against local core/log data or a regional normal-compaction-trend study before relying on the result. |
| OBG | psi/ft | Overburden (lithostatic) pressure gradient — the same gradient used by the Overburden Stress and Eaton Pore Pressure calcs. |
| Pn | psi/ft | Normal (hydrostatic) pore pressure gradient for the basin — the same gradient used by the Eaton Pore Pressure calc. |
| TVD | ft | True vertical depth of the point of interest. |
Assumptions
- Disequilibrium (under)compaction is the operative mechanism generating any departure from the normal compaction trend at this depth
- φ0 and c are correctly calibrated for the specific lithology and basin being analyzed — both vary significantly with clay mineralogy, depositional environment, and basin
- OBG and Pn (overburden and normal pore-pressure gradients) are representative of the basin and already established, e.g. from the Overburden Stress or Eaton Pore Pressure calcs
Limitations
- The exact numeric value of Athy's coefficient c is not a settled, universally-tabulated constant — published values vary by orders of magnitude across basins and lithologies, and the simple exponential form is known to over-predict compaction at great depth in some settings; treat any default as illustrative only and calibrate against local core/log data wherever possible
- Assumes a single compaction mechanism — other overpressure sources (fluid/hydrocarbon expansion, gas generation, aquathermal pressuring, lateral transfer) do not follow the same porosity-effective-stress relationship and are not captured here, the same caveat already disclosed by the Eaton Pore Pressure (sonic) calc for its own compaction-trend method
- A complementary, not a substitute, check against Eaton-style log-derived pore-pressure methods — Eaton (1975) and the equivalent-depth method (Magara, 1978) are methodologically distinct and independently calibrated; treat agreement or disagreement between the two as diagnostic information, not assume either is automatically more correct
- Does not account for cementation or other diagenetic porosity loss unrelated to compaction stress, which would make a rock appear over-compacted (lower porosity than the trend predicts) without a corresponding effective-stress signal
Use Cases
- → Cross-checking the Eaton Pore Pressure calc on the same well: Compare this porosity/density-log-based estimate against the Eaton Pore Pressure (sonic-based) calc on the same interval — agreement between independently-derived methods increases confidence; disagreement flags a method-specific issue or a non-compaction overpressure mechanism worth investigating.
- → Real-time overpressure monitoring while drilling: Track equivalent depth against actual TVD as new density/porosity data arrives while drilling, to catch a developing undercompacted (overpressured) zone before it becomes a well-control event.
- → Pre-drill geopressure prediction from offset density logs: Estimate likely pore pressure in a planned well using normal-compaction parameters calibrated from nearby, already-drilled offset wells.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Delaware Basin shales are predominantly normally-to-moderately overpressured rather than severely undercompacted in most areas — treat a strongly undercompacted result here as a flag to cross-check against the Eaton Pore Pressure calc and offset-well pressure data rather than accept at face value.
Gulf of Mexico
The classic setting for disequilibrium-compaction-driven overpressure — rapid Plio-Pleistocene sediment loading on low-permeability shale routinely produces strongly undercompacted, significantly overpressured intervals that this method was originally developed to diagnose.
Global
Athy's coefficient c and depositional porosity φ0 must be calibrated per basin and lithology — published values vary by orders of magnitude; never reuse a value from a different basin without independent verification.
References
Primary source
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