The drilling exponent (d), the exponent corrected for mud density (dc), and the exponent corrected for mud density and bit wear (dcs) are used to detect undercompacted shaly formations and associated high-pressure zones.

(1) d = uncorrected drilling exponent

when:
R = drilling rate (ft/hr)
K = rock drillability (~ 1 for shales)
N = rotary speed (rpm)
W = weight on bit (lb)
D = bit diameter (in.)

(2) dc = drilling exponent corrected for mud density

where:
d₁ = equivalent mud density of normal pore pressure gradient
d₂ = equivalent mud density of actual pore pressure gradient

(3) dcs = drilling exponent corrected for nmud density and bit wear.

Same as “dc” except that instead of R (drilling rate at time t) the drilling rate R_o (corrected for bit wear) is used.