### Calculate d-Exponent to Predict Pore Pressure Trends

This Excel spreadsheet calculates the d-exponent, a parameter used by drilling engineers to investigate ppore pressure trends when drilling into over-pressurized zones.

Normally, formation density increases with the drilling depth. But if the formation contains sand below the surface, then the drilling rate may increases with drilling depth. The d-exponent is used in several calculations to investigate these effects.

Jorden and Shirley (1966) suggested the d-exponent method, basing it on the Bingham equation. A later adjustment to the equation by Rehm and Mcledon (1971) included the effect of mud weight

The modified equation to calculate the d-exponent is

where
• c is the shale compactibility coefficient
• ρn is the mud weight equivalent (lb gal-1)
• ρm is the mud weight used (lb gal-1)
• D is drill bit diameter (in)
• W is the weight on the bit (x 1000 lb)
• R is the penetration rate (rpm)
• N is the rotary speed.
The d-exponent is often used in Eaton's equation

where
• P is the formation pore pressure (psi)
• Pob is the overburden pressure (ft)
• Z is the vertical depth (ft)
• d is the d exponent
• dn is the normal compaction trend of the d exponent
• Pp is the formation pore pressure (psi)
• Pp/Z is the normal pore pressure gradient (psi ft-1)