Oil and gas production
Productivity index and Vogel's IPR, bottomhole pressure from the fluid level, rod pump displacement and ESP head, water cut and oil in tonnes, gas-oil ratio, gas at standard conditions, chokes, decline forecast.
20 calculators
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).
J = q / (P_res − P_wf)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_bFlowing 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)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).
v = 2 · H_ref / t_refTheoretical 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 · nRequired 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_frProduction metering
Oil and water rates in m³/d and t/d from the metered liquid rate and water cut, the mixture density, and the conversion between volume and mass water cut.
q_o = q_l · (1 − W_v); Q_o = q_o · ρ_o; Q_w = q_l · W_v · ρ_wGas-oil ratio from the metered gas and oil rates — in m³/t, as in field reports, and in m³/m³.
G = Q_g / Q_oGas and chokes
Gas volume at 20 °C and 101.325 kPa (GOST 2939) from the volume at operating pressure and temperature, with the deviation factor; the gas formation volume factor. The same works for a flow rate: actual m³/h give standard m³/h.
V_st = V · (P / P_st) · (T_st / T) / ZLiquid rate of a flowing well at critical two-phase flow through the choke, from the tubing head pressure, the gas-liquid ratio and the choke size: the Gilbert, Ros, Baxendell and Achong correlations.
P_wh = A · R^B · q / S^CThe choke size that gives a target liquid rate of a flowing well at a known tubing head pressure and gas-liquid ratio (critical flow).
S = (A · R^B · q / P_wh)^(1/C)The critical gas velocity that lifts water or condensate droplets out of the well, and the matching minimum gas rate for a given tubing size — after Turner (with the +20 % adjustment) or Coleman (without it). Below this rate liquid accumulates at the bottom and loads the well up.
v_c = k · [σ · g · (ρ_l − ρ_g)]^(1/4) / √ρ_g; k = (40 / 0.44)^(1/4) = 3.09 (Coleman), × 1.2 (Turner)Production forecast
A model of one oil well from start-up to the economic limit: inflow to a vertical, deviated, horizontal or hydraulically fractured well, transient and pseudo-steady flow, the bubble point, a liquid-rate plateau, water cut and a material balance with depletion or pressure support. Monthly rate and pressure charts, a yearly table and CSV export.
J = 2π·k_h·h / (μ_o·B_o·(½·ln(4A / (γ·C_A·r_w²)) + s_eq)), γ = 1.781The rate after a given time and the cumulative production for exponential, hyperbolic or harmonic decline — from the initial rate, the first-year decline and the exponent b.
D_i = [(1 − D)^(−b) − 1] / b; b = 0: D_i = −ln(1 − D)The time for the rate to fall to the economic limit and the production until then — the well's remaining recoverable reserves from the decline curve.
t_ec = [(q_i / q_ec)^b − 1] / (b · D_i); b = 0: t_ec = ln(q_i / q_ec) / D_iOther areas
Hydraulic power from the flow rate and head, shaft power from the pump efficiency, power drawn from the supply, and the smallest motor rating with a margin.
P_h = ρ · g · Q · HFrom Mechanical engineeringFlow rate, head and power of a centrifugal pump at another speed — including an ESP or a pump on a variable speed drive — and with a trimmed impeller.
Q_2 = Q_1 · (n_2 / n_1) · (D_2 / D_1)From Mechanical engineeringStrokes per minute from the motor speed, the V-belt sheave diameters and the gearbox ratio, and the motor sheave diameter for a required stroke rate.
N = n_m · (d_m / d_r) · (1 − ε) / iFrom Mechanical engineeringVoltage drop in a three-phase or single-phase cable line from the conductor resistance at the operating temperature and the reactance, the power loss in the cable and the sending-end voltage — including a long ESP submersible cable.
R = ρ_20 · (1 + α · (t − 20)) · L / S, X = x_0 · LFrom Electrical engineeringElectricity to lift 1 m³ and 1 t of liquid by a pumping system — ESP, rod pump, injection or transfer pump — against a given head with the overall efficiency, and the daily consumption.
e = ρ · g · H / (3.6 · 10⁶ · η)From Electrical engineeringResults 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.