These series of formulas will determine the correct jet sizes when optimising for jet impact or hydraulic horsepower and optimum flow rate for two or three nozzles.
1. Nozzle area, sq in.: Nozzle area, sq in. = N12 + N22 + N32
1303.8
2. Bit nozzle pressure loss, psi (Pb): Pb = gpm2 x MW, ppg
b) For hydraulic horsepower: Popt = 1 x Pmax
Pmax b) For hydraulic horsepower: Qopt, gpm = (Popt )1 - M x Q1
Pmax
10858 x Pmax
9. To determine nozzles, 32nd in. for three nozzles:
10. To determine nozzles, 32nd in. for two nozzles:
Example: Optimise bit hydraulics on a well with the following:
Select the proper jet sizes for impact force and hydraulic horsepower for two jets and three jets:
DATA: Mud weight = 13.0 ppg Maximum surface pressure = 3000 psi Pump rate 1 = 420 gpm Pump pressure 1 = 3000 psi
Pump rate 2 = 275 gpm Pump pressure 2 = 1300 psi
Jet sizes = 17-17-17
1303.8
Nozzle area, sq in. = 0.664979
2. Bit nozzle pressure loss, psi (Pb):
10858 x 0.6649792
10858 x 0.6649792
3. Total pressure losses except bit nozzle pressure loss (Pc), psi:
4. Determine slope of line (M):
3000 Qopt = 297 gpm b) For hydraulic horsepower: Qopt, gpm = (1010) K 197 x 420
Pb = 1489 psi b) For hydraulic horsepower: Pb = 3000 psi — 1010 psi
10858x1489
Nozzles area, sq. in. = V 0.070927 Nozzle area, = 0.26632 sq. in.
b) For hydraulic horsepower: Nozzles area, sq. in. = V 2422 x 13.0
10858x1990
b) For hydraulic horsepower: Nozzles = V 0.1877 x 32
NOTE: Usually the nozzle size will have a decimal fraction. The fraction times 3 will determine how many nozzles should be larger than that calculated.
so: 1 jet = 10/32nds 2 jets = 11/32nds b) For hydraulic horsepower: 0.03 x 3 = 0.09 rounded to 0
2 x 0.7854
b) For hydraulic horsepower: Nozzles = V 0.1877 x 32
2 x 0.7854
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