Decline Curve & EUR Calculator

Arps decline (exponential / hyperbolic / harmonic) with closed-form EUR to an economic limit

Arps Decline EUR Production Forecast

Input Parameters

Initial production rate (generic rate units, e.g. bbl/d or Mscf/d).

Di is always a nominal ANNUAL decline. Per-day rates are multiplied by 365 so EUR is in the rate's own volume unit.

Entered as percent per year (e.g. 10 = 0.10 /yr).

0 = exponential, 0<b<1 = hyperbolic, 1 = harmonic.

Choose whether the forecast ends at an economic rate or a fixed number of years.

Same units as qi. Production stops when the rate drops to here.

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EUR (cumulative production)
Method: Arps (1945) decline. Cumulative (EUR) uses the closed-form integral of the rate equation for each regime. Units: Di is per year; per-day rates are converted with 365 days/year.
Disclaimer: This calculator is for educational and illustrative purposes only. Final reserves and production forecasts should be performed by qualified reservoir engineers using validated software and history-matched data.

About This Calculator

Decline curve analysis (DCA) is the workhorse of production forecasting and reserves estimation. The Arps (1945) equations describe how a well's production rate falls over time and provide closed-form expressions for cumulative production (the basis of the Estimated Ultimate Recovery, or EUR).

Rate vs Time

  • Exponential (b = 0): q(t) = qi · e−Dit
  • Hyperbolic (0 < b < 1): q(t) = qi · (1 + b·Di·t)−1/b
  • Harmonic (b = 1): q(t) = qi / (1 + Di·t)

Cumulative Production (EUR)

Integrating the rate from the initial rate down to the economic limit qlim gives the closed-form cumulative production:

  • Exponential: Np = (qi − qlim) / Di
  • Hyperbolic: Np = qib / [(1−b)·Di] · (qi1−b − qlim1−b)
  • Harmonic: Np = qi/Di · ln(qi/qlim)

Unit Handling

The nominal decline Di is always entered per year, so the closed-form cumulative comes out in (rate × year). When the rate is a per-day rate (e.g. bbl/d), the result is multiplied by 365 days/year so that EUR is expressed in the rate's own volume unit (barrels, Mscf, etc.). Choose "per-year" to skip that conversion.

Limitations

  • Boundary-dominated flow assumption — does not model transient or linear flow regimes.
  • Single-segment decline; multi-segment (e.g. b switching at a terminal decline) is not modelled.
  • Harmonic and hyperbolic EUR can be large; always cap with an economic limit or horizon.
  • Not a substitute for history-matched, probabilistic reserves estimation.

Need Professional Reserves & Forecasting Support?

For probabilistic decline analysis, multi-segment forecasts, type-curve generation, and field-level economics integration, we offer professional consulting with validated workflows.

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