Vogel IPR with the bubble point
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.
f(P) = P_res − P, P ≥ P_bf(P) = P_res − P_b + (P_b / 1.8) · [1 − 0.2 · (P/P_b) − 0.8 · (P/P_b)²], P < P_bJ = q_t / f(P_t); q = J · f(P_wf); q_max = J · f(0)Vogel's curve (1968) was derived for solution-gas drive without water: for wells with water it is applied to the oil rate, and at a high water cut it understates the liquid rate at low bottomhole pressures. Use a stabilized test; all pressures on one scale (absolute or gauge).
Source: Vogel J.V., Inflow Performance Relationships for Solution-Gas Drive Wells, JPT, 1968; composite IPR — Economides M.J. et al., Petroleum Production Systems, ch. 3
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
From the latest shut-in survey (build-up), referred to the mid-perforation depth.
From the PVT analysis of a bottomhole sample at reservoir temperature. If P_b is not below the reservoir pressure, the reservoir is saturated and Vogel's curve is used alone.
At stabilized flow.
A downhole gauge, or calculated from the fluid level — at the same depth as the reservoir pressure.
Unit converter for this formulaPressure · Liquid rate · Productivity index
- 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.
- q_max — Absolute open flow (AOF, at P_wf = 0)–
- q_b — Rate at a bottomhole pressure equal to the bubble point–
- J — Productivity index (above P_b)–
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).
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.
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.