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Decline Curve Fitting Tool: Fit Arps Decline & Forecast EUR

Paste monthly production · fit Arps qi, Di, b · forecast EUR to an economic limit

Fit an Arps decline curve to your monthly production
Paste monthly production (one value per line, or two columns from a spreadsheet). The tool fits exponential, hyperbolic and harmonic decline by least squares on the log of rate, picks the best model, and forecasts EUR to your economic-limit rate. Then send the fitted parameters straight to the Well Economics calculator.

Production data

Fit & forecast settings

%
yr

Zero-rate (shut-in) months are skipped in the fit but keep their place in time; a blank cell between months is read as zero. Commas inside numbers (1,234) are read as thousands separators, so separate columns with tabs or spaces. At least 6 producing months are needed; 12+ is much better.

Key Relations

q(t) = qi / (1 + b·Di·t)^(1/b)
Exponential (b = 0) · Harmonic (b = 1)
Secant effective decline (SPEE REP 6) De = 1 − (1 + b·Di)^(−1/b)
Fit: minimize Σ [ln qobs − ln qmodel]²
EUR = cumulative to date + forecast to the limit rate

Standards & References

  • Arps, J.J. (1945)
    “Analysis of Decline Curves,” Trans. AIME 160
  • SPEE Recommended Evaluation Practice #6
    Definition of decline-curve parameters: secant and tangent effective decline
  • SPE-PRMS
    Reserves definitions; decline-curve analysis as a production-performance method

Engineering Notes

  • Short histories fit many curves. With under a year of data, b is poorly determined and EUR can swing widely.
  • A best-fit b above 1 usually reflects transient flow in tight rock. The terminal decline caps the long tail.
  • By default the fit starts at the peak month, so qi is the rate at that point. The Well Economics hand-off treats that point as time zero of a new well, so it is a type curve from the fit start, not a forecast from today. Ramp-up months are counted in cumulative production but not in the fit.
  • Screening tool: does not model choke changes, interference, workovers or flow regimes. Not a reserves report.

How to Fit a Decline Curve

  1. Paste your production. Use monthly average daily rates or monthly volumes, oldest month first. A column copied from Excel works, and two columns (month, value) are accepted.
  2. Choose the fit start and limits. Starting at the peak month skips ramp-up. Set the economic-limit rate at which the well would be shut in, and a terminal decline of 5-8% for the long tail.
  3. Check the fit, then use it. Look at the curve against your data and the comparison table. If it looks right, send qi, decline and b to the Well Economics calculator for NPV, IRR and breakeven.

Frequently Asked Questions

How do you fit an Arps decline curve?

Choose the decline model (exponential, hyperbolic or harmonic) and adjust qi, the initial decline Di and the exponent b to minimize the difference between the model rate and the observed rate. This tool minimizes the squared error of the natural log of rate, so early high-rate months do not dominate the fit.

What b factor should I use?

b = 0 is exponential decline, b = 1 harmonic, and values between are hyperbolic. Conventional wells often fit b between 0 and 0.5; unconventional wells often fit 1 or higher during transient flow. Because a large b overstates the long tail, practitioners cap b (this tool defaults to 1.5) and apply a terminal exponential decline.

What is the difference between nominal and effective decline?

Nominal decline Di is the instantaneous rate in the equations. Effective decline is an annual percentage, defined two ways (SPEE REP 6). This tool reports secant effective decline, the actual drop in rate over the first year: De = 1 - (1 + b*Di)^(-1/b), or 1 - exp(-Di) for exponential. Tangent effective decline is 1 - exp(-Di) for any b.

How much data do I need?

At least 6 producing months, but 12 to 24 or more is far better. With a short history many combinations of b and Di fit equally well and the EUR forecast is uncertain.

Is the EUR a reserves estimate?

No. It is a screening forecast from a curve you fit to past production. Reserves classification requires the full SPE-PRMS process, reservoir data and economic assumptions.