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.
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)
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