Bottomhole pressure from the fluid level
Flowing bottomhole pressure and pump intake pressure of a rod-pumped or ESP well from the casing pressure and the annular fluid level: oil in the annulus above the pump intake, the produced mixture below it.
P_in = P_c + ρ_a · g · (H_pump − H_dyn)P_wf = P_in + ρ_l · g · (H_perf − H_pump)ρ_l = ρ_o · (1 − W) + ρ_w · WThe weight of the annular gas column (about 0.08 MPa per 1 000 m at a casing pressure of 1 MPa) and the gas in the liquid are neglected: with a foamy column above the intake the true pressure is lower. All depths are vertical. With the pump below the perforations the second term is negative and the formula still holds.
Source: Hydrostatic equation; the field method for acoustic fluid level surveys
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
From the wellhead gauge; enter it as gauge and the results are gauge too.
Depth of the annular fluid level from an echometer survey. All depths are vertical (use the survey for a deviated well).
Degassed oil in the annulus — the separated oil density is usually taken, 800–900 kg/m³.
Formation water is usually 1 010–1 180 kg/m³; take it from the water analysis.
In a producing well the water drains from the annulus to the intake, so there is usually oil above it.
Unit converter for this formulaPressure · Length · Density and °API · Fraction and percent
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- P_in — Pump intake pressure–
- h_sub — Pump submergence below the fluid level–
- ρ_l — Density of the produced mixture–
More in Inflow and productivity
Productivity index from a stabilized rate and flowing bottomhole pressure, the drawdown, and the rate at another bottomhole pressure (straight-line IPR).
Oil rate at any bottomhole pressure and the absolute open flow (AOF) from one test: a straight line above the bubble point, Vogel's curve below it. For a saturated reservoir (P_b ≥ P_res) it is Vogel's curve alone.
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.