Decline Curve Analysis (Arps)
Paste production history (date or time in days, rate) to fit the Arps equations by least squares, plot the forecast and compute the estimated ultimate recovery (EUR) to the economic limit.
This tool runs entirely in your browser: your data is not uploaded to any server. Free, no signup.
Educational tool for preliminary analysis. It is not a substitute for certified software or a qualified engineer’s review for major decisions.
Format: two columns separated by comma, semicolon or space: date (YYYY-MM-DD or DD/MM/YYYY) or time in days, then rate (STB/d, Mscf/d…). Lines starting with # are ignored.
Results
Calculation steps and intermediate values
Explanation and formulas
Arps (1945) assumes the nominal decline D = −(dq/dt)/q changes with rate through the exponent b: b = 0 is exponential (constant percentage), b = 1 harmonic, and values in between hyperbolic.
The tool finds qi, Di (and b in auto mode) that minimise the sum of squared rate residuals; qi is solved analytically for each (Di, b) pair. Time zero is the first data point.
The equations apply to boundary-dominated flow under constant operating conditions. b > 1 (transient flow in unconventional wells) is not supported because it gives an unbounded EUR.
q(t) = qi / (1 + b·Di·t)^(1/b) (0 < b < 1)
q(t) = qi / (1 + Di·t) (b = 1)
Np = (qi − q)/Di | qi^b/((1−b)·Di)·(qi^(1−b) − q^(1−b)) | (qi/Di)·ln(qi/q)
t_el = ln(qi/qa)/Di | ((qi/qa)^b − 1)/(b·Di)
min Σ (q_obs − q_model)²
Validation
Published example (Example #3 in “Reserve Estimation Methods – Decline Curve Analysis” course notes): a well declines from 100 to 96 BOPD in one month, exponential decline. Book: D = 0.040822 /month, 61.27 BOPD after 12 months, 39.91 BOPD after 22.5 months, 28,858 STB in one year. Tool: 0.040822, 61.27, 39.91 and 28,857 STB (rounding), and the fit recovers D = 0.040822 and b = 0 from the monthly example data. The q and Np equations also match a reference table (qi = 1000, Di = 0.001/d, t = 365 d) for b = 0, 0.5 and 1: 694.1967, 715.1509 and 732.6007 STB/d.
References
- Arps, J.J. (1945). Analysis of Decline Curves. Transactions of the AIME 160(1): 228–247. SPE-945228-G.
- Ahmed, T. (2019). Reservoir Engineering Handbook, 5th ed., Gulf Professional Publishing — decline curve analysis chapter.
- Fetkovich, M.J. (1980). Decline Curve Analysis Using Type Curves. JPT 32(6): 1065–1077. SPE-4629-PA.
- SPE PetroWiki: Production forecasting decline curve analysis.