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INPUT   DATA

Title

Mud weight		ppg
Nozzle size #1		1/32th inch
Nozzle size #2		1/32th inch
Nozzle size #3		1/32th inch
Max surface pressure		psi
Pump pressure 1		psi
Pump rate 1		gpm
Pump pressure 2		psi
Pump rate 2		gpm

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OUTPUT   VARIABLES   &   GRAPHS

Optimum	Impact Force	Horsepower
♦  Pressure loss (psi)
♦  Flow rate (gpm)
♦  3-Nozzle bit diameters (1/32th in.)
♦  2-Nozzle bit diameters (1/32th in.)

Bit Nozzle Selection - Optimized Hydraulics

The necessary conditions for attaining optimal bottomhole cleaning below a drill bit is usually approximated via the optimization of two design criteria: Hydraulic Impact force and Bit Hydraulic horsepower. The process involves running a circulating pressure test at the rig site, while keeping the rotary speed and weight-on-bit constant. The test involves varying the mud pump speed and recording the pump pressure and circulating rate at each speed. It is assumed here that the test is conducted at 2 speeds, #1 & #2. The objective is to determine the optimum pressure drop across the bit nozzles and the optimum flow rate, and from thence determine the nozzle sizes to support these optimum conditions.

The calculation steps begins with the estimation of nozzle pressure drop for each test point (P_b1 & P_b2) from the equation:

P_b is then used to derive the "slope" M, which is given by:

The optimum nozzle pressure loss is given by the expression:

The optimum circulation rate is given by the expression:

The optimum nozzle area is is then computed via by the expression:

Finally, nozzle jet diameters for 2- and 3-nozzle bits are then computed and rounded-up to the nearest ¹/₃₂th inch.

Where:

   Q = mud circulation rate, gallons/min.
   Q_opt = optimum circulation rate, gallons/min.
   P = surface pump pressure, psi
   P_max = maximum surface pump pressure, psi
   P_b = bit pressure loss, psi
   A_n = total nozzle area, sq.inch.
   ρ = mud weight, ppg
   M = derived parameter of circulation experiment, dimensionless

BIBLIOGRAPHY

• Moore P.L.; Drilling Practices Manual; Pennwell Books, Tulsa, Oklahoma, 1986, chap. 7.
• Lapeyrouse N.J.; Formulas & Calculations for Drilling, Production and Workover; Gulf Professional Publ. Co, Amsterdam, 2002, chap.5.
• Mitchell B.; Advanced Oilwell Drilling Handbook; Mitchell Engineering, Lakewood, Colorado, 1995.
• Mian M.A.; Petroleum Engineering Handbook For the Practicing Engineer; Pennwell Publ Co, Tulsa, 1992, vol II, chap. 8.