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
- ρ
_{n}is the mud weight equivalent (lb gal^{-1}) - ρ
_{m}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)
- P
_{ob}is the overburden pressure (ft) - Z is the vertical depth (ft)
- d is the d exponent
- d
_{n}is the normal compaction trend of the d exponent - P
_{p}is the formation pore pressure (psi) - P
_{p}/Z is the normal pore pressure gradient (psi ft^{-1})

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