Bit calculations

1. Bit Calculations
Units
Where:
Pb = Bit Pressure Drop (lbs/in2
)
MW = Mud Weight (ppg)
Q = Flow Rate (gpm)
An = Total Nozzle Area (in2
)
Vn = Nozzle Velocity (ft/sec)
HHPb = Horse Power at bit (hp)
HSI = Horse Power per inch (hp/in2
)
Db
= Bit Diameter (in)
Ab = Area of Bit (in2
)
lfb = Impact Force at bit (lbf)
Vc = Cross Flow Velocity (ft/sec)
N = Number of Nozzles
Es = Specific Energy (psi)
µ = Coefficient of Friction
ROP = Rate of Penetration (ft/hr)
WOB = Weight on Bit (lbf)
T = Torque (ft-lbs)
Ah = Area of Hole (in2
)
MSE = Mechanical Specific Energy (psi)
Cd = Nozzle discharge coefficient
Pressure Drop Across Bit (psi)
Calculated From Flow Rate, assumes Cd=1.0:
Pb =
(MW)(Q2
)
(12,032)(An2
)
Calculated FromVelocity:
Pb =
(MW)(Vn2
)
(1,239)
Bit Nozzle Velocity (ft/sec)
Calculated From Flow Rate:
Vn = (0.321)
(Q)
(An)
Calculated From Pressure Drop:
Vn = [
(1,239)(Pb)
]
1/2
(MW)
Total Bit Nozzle area (in2
)
Calculated From Bit Pressure Drop:
An = [
(MW)(Q2
)
]
1/2
(12031)(Pb)
An = ∑(An1
+ An2
+ ...Anx
)
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
Impact of Jet Nozzles on Hole Bottom (lbf)
Calculated FromVelocity:
lfb =
(Q)(MW)(Vn)
(1930)
Calculated From Pressure Drop:
lfb = 0.0173Q [Pb
MW] 1/2
Cross Flow Velocity under the Bit (ft/sec)
Vc = [
(108.5) (Q)(Vn)
]
1/2
(NDb
)
Mechanical Specific Energy using µ (psi)
MSE =WOB[
1
+
(13.33)(µ)(RPM)
]Ab (ROP)(Db)
Bit Aggressiveness/Coefficient of Friction
µ = [
36(T)
](WOB)(Db)
Mechanical Specific Energy usingTorque (psi)
MSE =
480(T)(RPM)
+
1.274(WOB)
ROP(Db2
) (Db2
)
BitTorque (ft-lbs)
T=
µ(Db)(WOB)
36
Minimum Flow rate for PDC Bits (gpm)
GPM = 12.72Db
1.47