Bit Calculations

Bit Calculations Units Where: Pb MW Q An Vn HHPb HSI Db Ab lfb

= Bit Pressure Drop (lbs/in2) = Mud Weight (ppg) = Flow Rate (gpm) = Total Nozzle Area (in2) = Nozzle Velocity (ft/sec) = Horse Power at bit (hp) = Horse Power per inch (hp/in2) = Bit Diameter (in) = Area of Bit (in2) = Impact Force at bit (lbf)

Pressure Drop Across Bit (psi) Calculated From Flow Rate, assumes Cd=1.0:

Pb =

(MW)(Q ) (12,032)(An2) 2

Vc N Es µ ROP WOB T Ah MSE Cd

= = = = = = = = = =

Cross Flow Velocity (ft/sec) Number of Nozzles Specific Energy (psi) Coefficient of Friction Rate of Penetration (ft/hr) Weight on Bit (lbf) Torque (ft-lbs) Area of Hole (in2) Mechanical Specific Energy (psi) Nozzle discharge coefficient

Impact of Jet Nozzles on Hole Bottom (lbf) Calculated From Velocity:

lfb =

(Q)(MW)(Vn) (1930)

Calculated From Velocity:

Calculated From Pressure Drop:

(MW)(Vn ) Pb = (1,239)

lfb = 0.0173Q [PbMW] 1/2

2

Bit Nozzle Velocity (ft/sec) Calculated From Flow Rate:

Vn = (0.321)

(Q ) (An)

Calculated From Pressure Drop:

Vn =

[

(1,239 )(Pb ) (MW)

1/2

]

Total Bit Nozzle area (in2) Calculated From Bit Pressure Drop:

(MW )(Q2 ) 1/2 (12031)(Pb) An = ∑(An1+ An2 + ...Anx ) An =

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]

Bit Hydraulic Horsepower (hp) Hydraulic HP by Bit Nozzles:

HHPb =

(Pb )(Q) (1714)

Hydraulic HP per sq. in. of Bit Diameter:

HSI =

(HHPb)(1.273) (Db ) 2

Cross Flow Velocity under the Bit (ft/sec) (108.5) (Q)(Vn) 1/2 Vc = (NDb )

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Mechanical Specific Energy using µ (psi) 1 (13.33)(µ)(RPM) MSE =WOB + Ab (ROP)(Db)

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Bit Aggressiveness/Coefficient of Friction 36(T) µ= (WOB)(Db)

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Mechanical Specific Energy using Torque (psi) 480(T)(RPM) 1.274(WOB) MSE = + ROP(Db2) (Db2) Bit Torque (ft-lbs) µ(Db)(WOB) T= 36 Minimum Flow rate for PDC Bits (gpm) GPM = 12.72Db1.47