drilling · pressure
Corrected d-Exponent
click formula to derive ↑
Inputs
ft/hr
rpm
lbf
in
lb/gal
lb/gal
Description
Computes the drilling-exponent pore pressure indicator from routine drilling parameters (ROP, rotary speed, weight on bit, bit diameter), corrected for mud-weight-differential effects on penetration rate — the composite Jorden & Shirley (1966) / Rehm & McClendon (1971) method actually used in field practice. A different data source (drilling performance) from eaton_pp/eaton_resistivity's log-based methods, but the same pore-pressure-detection intent.
Variables
| Symbol | Unit | Description |
|---|---|---|
| d | — | d-Exponent |
| dxc | — | Corrected d-Exponent |
| R | ft/hr | Instantaneous rate of penetration while drilling the interval of interest. |
| N | rpm | Rotary table (or top drive) rotational speed while drilling the interval of interest. |
| W | lbf | Weight applied to the bit while drilling the interval of interest. |
| D | in | Diameter of the bit drilling the interval of interest. |
| MWn | lb/gal | Mud weight that would be normal (hydrostatic-balanced) for the basin at this depth — the Rehm & McClendon (1971) correction baseline. |
| MWa | lb/gal | Actual mud weight in use while drilling the interval of interest. |
Assumptions
- The interval drilled is predominantly shale — the d-exponent method is calibrated for shale and is less reliable in sands, carbonates, or evaporites
- Bit type, bit wear, and hydraulics are reasonably consistent across the interval used to establish the normal trend, since the d-exponent does not correct for these
- The normal mud weight (MWn) reflects the actual hydrostatic-balanced mud weight for the basin at this depth, not just the mud weight used earlier in the well
Limitations
- A single dxc value cannot itself confirm overpressure — it must be compared against a normal trend fitted from offset wells in normally pressured, normally drilled sections at similar depths
- Bit wear, bit type changes, formation lithology changes, and drilling hydraulics all affect ROP independent of pore pressure and are not corrected for by dxc
- Least reliable in soft, poorly consolidated, or highly interbedded formations where ROP is dominated by lithology rather than compaction state
Use Cases
- → Real-time drilling-break monitoring: Track dxc continuously while drilling to flag a departure from the normal trend (a 'drilling break') as an early real-time overpressure indicator, ahead of mud logging gas shows.
- → Cross-check against log-based Eaton methods: Compare dxc's trend against the sonic-based (eaton_pp) or resistivity-based (eaton_resistivity) predictions, since d-exponent uses an entirely independent data source (drilling performance, not wireline/LWD logs).
- → Offset-well normal trend calibration: Establish a basin-specific normal dxc-versus-depth trend from normally pressured offset wells to calibrate overpressure detection for the next well.
Related Calculations
Region Notes
Gulf Coast
The original Jorden & Shirley (1966) and Rehm & McClendon (1971) papers were both calibrated to Gulf Coast Tertiary shale sections — the classic dxc-versus-depth drilling-break application area.
Permian Basin
Frequent bit type and mud system changes across Delaware/Midland Basin intervals can break the dxc trend independent of pore pressure — re-anchor the normal trend after any bit or mud program change.
References
Primary source
Primary source
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