Drilling guides › Bit hydraulics: TFA, nozzle velocity, HSI and impact force
Bit hydraulics: TFA, nozzle velocity, HSI and impact force
Every gallon the mud pumps deliver ends up going through the bit nozzles, and the pressure spent there is the only part of the pump's work that does anything useful at the bottom of the hole. The jets clean cuttings off the cutters, sweep the hole bottom so the bit is not regrinding old chips, and in softer rock help to drill it directly. Too little energy at the bit and the cutters ball up and the rate of penetration falls; too much pressure drop and you run out of pump pressure before reaching the flow rate the hole needs for cleaning. Picking nozzles is the way to balance the two.
Total flow area
Nozzle sizes are given in 32nds of an inch, so a "12" nozzle has a 12/32 in (0.375 in) diameter. The total flow area (TFA) is the sum of the areas of all the nozzles on the bit, plus any fixed ports.
| Size (1/32 in) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|
| Area (in²) | 0.0621 | 0.0767 | 0.0928 | 0.1104 | 0.1296 | 0.1503 | 0.1726 | 0.1963 |
In metric, nozzle diameter in millimetres is the size × 0.79375, and 1 in² = 645.16 mm².
Pressure drop, velocity, power and force
The 10,858 constant already contains a nozzle discharge coefficient of 0.95 (12,032 × 0.95²); some software uses a slightly different coefficient, so expect small differences. 1,714 converts psi × gpm to horsepower. HSI, the hydraulic horsepower per square inch of hole bottom, is the easiest number to compare between bit sizes.
Notice what the formula says: bit pressure drop rises with the square of flow rate and falls with the square of TFA. Doubling the flow with the same nozzles needs four times the pressure at the bit, and going one nozzle size bigger on every jet takes a sizeable chunk off it.
Worked example 1: hydraulics of a 12-1/4 in PDC bit
A 12-1/4 in PDC bit with six 13/32 in nozzles, pumping 800 gpm of 12.0 ppg mud. Standpipe pressure is 3,200 psi.
This is a workable setup. The 330 ft/s jet velocity is in the range most programmes look for, and the HSI is moderate. Smaller nozzles would put more of the standpipe pressure to work at the bit, if the pump has the pressure to spare.
How to choose nozzles
Start from the flow rate, not the nozzles. The flow rate is set first by hole cleaning: annular velocity, cuttings transport in deviated sections, and the needs of the motor or rotary steerable tool. Then:
- Find the maximum working pressure for the pumps and surface equipment, and keep a margin below it for pressure that builds up as the hole deepens or the mud gets heavier.
- Work out the pressure lost everywhere except the bit at that flow rate: surface lines, drill string, BHA tools, motor and annulus. These are the parasitic losses, taken from a hydraulics program or measured with the bit off bottom and nozzles known.
- The pressure left over is your budget for the bit. Calculate the TFA that uses it: TFA = √(MW × Q² ÷ (10,858 × Bit ΔP)).
- Pick a nozzle combination at or just above that TFA, so you do not exceed the budget, and recalculate the hydraulics with the real TFA.
Two classic rules of thumb guide the split. When the goal is maximum hydraulic horsepower at the bit, the bit pressure drop should be about 65% of the standpipe pressure. When the goal is maximum jet impact force, it should be about 48%. Both come from optimising with a fixed surface pressure and flow rate free to change, so treat them as targets to aim for, not as hard limits. In practice many wells end up below them because hole cleaning or the motor sets the flow and the pump sets the pressure.
Worked example 2: choosing nozzles for an 8-1/2 in section
An 8-1/2 in PDC bit with five nozzle ports. Planned flow 500 gpm of 10.5 ppg mud. The pump working limit is 3,800 psi and the parasitic losses at 500 gpm are 2,300 psi.
Choose two 11s and three 10s. With them:
The HSI is high for this bit size, which helps in a sticky shale but leaves only a small pressure margin. If the mud is due to be weighted up during the section, both the parasitic losses and the bit drop will rise, so one size larger on a nozzle or two may be the better choice.
Reading the hydraulics on the rig
A sudden drop in standpipe pressure at constant flow can mean a lost nozzle or a washout in the string; a rise can mean a plugged nozzle or a balled bit. Because bit pressure drop follows the square of TFA, losing one nozzle out of six changes the bit drop by far more than one-sixth, which is why a lost jet is usually easy to see on the gauge. Compare the standpipe pressure with the value calculated from the known nozzles each time the flow rate or mud weight changes.
Common mistakes
- Adding nozzle diameters instead of nozzle areas.
- Forgetting fixed ports or a blanked port when working out TFA.
- Choosing nozzles first and then reducing flow below what hole cleaning needs to keep pressure in range.
- Leaving no pressure margin for deeper hole, heavier mud or a motor stall.
- Using a different discharge coefficient from the one your hydraulics software uses, then wondering why the numbers do not match.