Bourgoyne and Young ROP Calculator: Eight-Factor Penetration Rate Model

Ask why the bit is drilling slowly and you will get eight different answers from eight different specialists: the rock got harder, the mud is too heavy, the bit is dull, not enough weight, not enough RPM, poor hydraulics, abnormal pressure, deep compacted section. The lasting achievement of Bourgoyne and Young in 1974 was refusing to pick one: their model multiplies all eight effects together, each as its own function, and lets regression against offset well data decide how strongly each one matters in a given field. Half a century later it remains the reference point that newer machine-learning ROP models are benchmarked against.

The eight functions in brief

• f1 sets the baseline formation drillability, the ROP under standard conditions
• f2 and f3 handle compaction: the normal slowdown with depth, plus a boost in undercompacted, abnormally pressured intervals
• f4 is the differential pressure term, an exponential penalty for drilling overbalanced that is often the single biggest lever
• f5 and f6 are the operator’s knobs: weight on bit above a threshold, and rotary speed, each with a power-law exponent
• f7 discounts for tooth wear as the bit dulls, and f8 credits jet impact force for keeping the bottom clean

Worked example

At 10,000 ft with a 9.5 ppg pore gradient and 10.0 ppg ECD, running 4 klb per inch of bit diameter at 100 rpm on a bit at 30 percent tooth wear with 1,000 lbf of jet impact, the mid-range default coefficients predict about 17.6 ft/hr. The factor breakdown the calculator displays is the diagnostic part: here f4 = 0.61 reveals that the half-pound of overbalance is quietly costing four of every ten feet per hour the well could be making, a bigger effect than the dull bit (f7 = 0.89) that would probably get blamed on the morning call.

Using the model honestly

Two things make this model useful and one thing makes it dangerous. Useful first: the multiplicative structure means the factor display doubles as a sensitivity analysis, showing exactly which lever pays before you touch anything; and the model is deliberately calibratable, with a1 through a8 meant to be regression-fitted from local drilling data rather than copied from a book. The danger is using the default coefficients as if they were physics constants: they are mid-range values from the original literature, tuned to roller-cone bits in Gulf Coast sediments, and a PDC bit in an unconventional play obeys different arithmetic (the tooth wear function in particular assumes milled-tooth wear behavior). Fit the coefficients to your offsets and the model earns real predictive power; skip the calibration and treat the output as a structured way to reason about relative changes, not absolute feet per hour.

Related Calculators and Reference

The efficiency-focused view of the same problem is the MSE optimization calculator, the jet impact force input comes from the bit hydraulics calculator, and the overbalance that f4 penalizes is set by mud weight against the pore and fracture gradient window. The PetroWiki page on rate of penetration discusses the model and its calibration.