The original “d” exponent is good for constant mud weight but in reality several drilling operations drill with various mud weights in hole due to weight up. In order to account for mud weight variation, so modification of d exponent, called “corrected d exponent”, has been made to correct for mud weight changes.
The corrected d-exponent is listed below.
dc = log (R ÷ 60N) ÷ log (12W ÷ 1000D) x (MW1 ÷ MW2)
Where;
dc = corrected “d” exponent
R = penetration rate in feet per hour
d = exponent in drilling equation, dimensionless
N = rotary speed in rpm
W = weight on bit in kilo pound
D = bit size in inch
MW1 = initial mud weight in ppg
MW2 = actual mud weight in ppg
Example: Determine the corrected d-exponent from following information.
Rate of penetration (R) = 90 ft/hr
Rotary drilling speed (N) = 110 rpm
Weight on bit (W) = 20 klb
Bit Diameter (D) = 8.5 in
MW1 = 9.0 ppg
MW2 = 12.0 ppg
Solution: dc = log [90÷ (60 x 110)] ÷ log [(12 x 20) ÷ (1000 x 8.5)] x (9.0 ÷ 12.0)
dc = 1.20 x 0.75
dc = 0.9
** Please remember that single d exponent or corrected d exponent valve does not help identify abnormal pressure. The trend of d exponent will help drilling personnel detect high formation pressure zones while drilling.
Please find the excel sheet for calculating the corrected D Exponent
Ref book: 
Formulas and Calculations for Drilling, Production and Workover, Second Edition
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June 4th, 2010 at 9:51 pm
[...] Normally, trends of d-Exponent will increase as we drill deeper, but this value will decrease to lower values than what we expect in transition zones. By closely monitored d-Exponent, d-Exponent chart will be useful for people on the rig to notify the high pressure transition zones. Read and understand about d-Exponent and learn how to calculate d-Exponent and normalized d-Exponent (corrected d-Exponent) [...]