ESP: total dynamic head, stages and power
Required ESP head from the fluid level, the wellhead pressures and the tubing friction; the number of stages from the head per stage, the hydraulic power, the shaft power and the electrical input of the submersible motor.
H = H_dyn + (P_wh − P_c) / (ρ · g) + h_frZ = ⌈H / h_st⌉N_h = ρ · g · Q · HN_sh = N_h / η_p; N_el = N_sh / η_mThe head is in metres of the pumped liquid. Gas (the lighter column in the tubing and the head loss on a gassy mixture) and viscosity are not included — correct the pump curve for viscous oil. Cable and transformer losses are not in N_el; select the motor with a power margin.
Source: API RP 11S4 (ESP sizing and selection); Brown K.E., The Technology of Artificial Lift Methods
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Vertical depth of the level at which the inflow equals the pump rate (from the productivity index).
The flowline pressure the pump works against; usually 1–2.5 MPa.
Of the water-oil mixture at the well's water cut.
For 2-7/8 in tubing (62 mm ID) at 100 m³/d of water, about 3 m per 1 000 m; they grow roughly as the rate squared.
From the pump curve; usually 4–6 m for 5-series (4.56 in) pumps.
At the operating point, from the curve: 0.4–0.65.
Induction motor 0.80–0.88, permanent-magnet motor about 0.9.
Unit converter for this formulaLiquid rate · Length · Pressure · Density and °API · Power · Fraction and percent
- 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.
- Z — Number of stages–pcs
- N_h — Hydraulic power–
- N_sh — Pump shaft power–
- N_el — Motor electrical input–
More in Artificial lift
Depth of the annular fluid level from the travel time of the reflected acoustic pulse; the speed of sound comes from the echo of a marker at a known depth (a marker sub or the tubing collars).
Theoretical and actual displacement of a sucker-rod pump from the plunger diameter, stroke length and pumping speed, with the volumetric efficiency.
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.