Sucker-rod pump displacement
Theoretical and actual displacement of a sucker-rod pump from the plunger diameter, stroke length and pumping speed, with the volumetric efficiency.
Q_t = 1440 · (π · D² / 4) · S · nQ = η · Q_tS is the polished rod stroke. The plunger stroke differs from it by the rod and tubing stretch under the fluid load and by dynamic effects; these, with slippage and gas, are in the volumetric efficiency η.
Source: API RP 11L: PD = 0.1166 · S_p · N · D² (bbl/d, S and D in inches); plunger sizes — API Spec 11AX
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Common API 11AX sizes: 1-1/16, 1-1/4, 1-1/2, 1-3/4, 2-1/4, 2-3/4, 3-3/4 in.
From the pumping unit data: usually 1.2–3.5 m for beam units, up to 6–7 m for long-stroke units.
Usually 3–10 strokes per minute.
Usually 0.6–0.85: slippage, gas at the intake, rod and tubing stretch.
Unit converter for this formulaLength · Liquid rate · Fraction and percent
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- Q_t — Theoretical displacement–
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).
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.
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.