Time to the economic limit and remaining reserves (Arps)
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_iN_p = q_i^b · (q_i^(1−b) − q_ec^(1−b)) / ((1 − b) · D_i); b = 0: (q_i − q_ec) / D_i; b = 1: (q_i / D_i) · ln(q_i / q_ec)D_i = [(1 − D)^(−b) − 1] / b; b = 0: D_i = −ln(1 − D)Extrapolating the decline assumes unchanged operating conditions: no well interventions, no change in the well's regime or the pressure maintenance. D is the actual rate drop over the first year; a year is 365 days. For a full well model — from the reservoir and the well type to a yearly production profile — see the Well production profile calculator.
Source: Arps J.J., Analysis of Decline Curves, Trans. AIME, vol. 160, 1945
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
The actual drop: 20 % means that after a year the rate is 0.8 · q_i.
0 is exponential, 1 harmonic, in between hyperbolic; fit it to the production history.
The rate at which the revenue equals the well's operating costs, taxes included.
Unit converter for this formulaLiquid rate · Time · Liquid volume · 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.
- N_p — Production to the economic limit (remaining reserves)–
More in 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.
The 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.
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.