Bit hydraulics: nozzles, pressure drop and power
Total flow area (TFA), jet velocity, bit pressure drop, hydraulic power at the bit and per unit of hole area (HSI), jet impact force.
TFA = π/4 · (n_1 · d_1² + n_2 · d_2²)v_n = Q / TFAΔP_b = ρ · v_n² / (2 · C_d²)N_b = ΔP_b · Q; HSI = N_b / (π/4 · D_b²)F_j = ρ · Q · v_nIn field units ΔP (psi) = ρ (ppg) · Q² (gpm) / (10 858 · TFA² (in²)) — that is C_d = 0.95; the constant 12 031 corresponds to C_d = 1. By the classic criteria (Kendall, Goins) bit hydraulic power peaks when about 65 % of the pump pressure is spent across the bit, jet impact force at about 48 %.
Source: Bourgeois et al., Applied Drilling Engineering (SPE, 1986), ch. 4; Kendall H. A., Goins W. C., Trans. AIME (1960)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
12/32 in = 9.525 mm; field units show 32nds of an inch.
0 if all nozzles are the same size.
Usually 0.95.
Unit converter for this formulaLiquid rate · Density and °API · Length · Pressure · Area · Velocity · Power · Force and load
- m³/d1
- m³/h0.0416667
- L/s0.0115741
- L/min0.694444
- m³/min0.000694444
- bbl/d6.28981
- Mbbl/d0.00628981
- ft³/d35.3147
- US gpm0.183453
- bbl/min0.00436792
A day is 24 hours.
- TFA — Total flow area–
- v_n — Jet velocity–
- N_b — Bit hydraulic power–
- HSI — Hydraulic power per hole area–W/mm²
- HSI — The same in field units–hp/in²
- F_j — Jet impact force–
More in Hydraulics
Output per stroke and flow rate of a single-acting triplex or quintuplex pump from the liner size, stroke length, pump speed and volumetric efficiency.
Average mud velocity in the annulus between the hole (or casing) and the pipe at a given pump rate.
Pump strokes and time to pump the string and annulus volumes: when the mud reaches the bit, when the bottoms-up (cuttings, gas) reaches surface, and how long a full circulation takes.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.