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Arps Decline Curve Forecast Calculator

Forecast production rate and cumulative oil with exponential, hyperbolic and harmonic decline over a defined time horizon.

Inputs

Results

Calculate to view linked results. Default values are examples, not recommended operating inputs.

Learn, compare and practice

Worked explanations, controlled studies and printable exercises connected to this calculation.

Exponential hyperbolic and harmonic decline explainedHow the hyperbolic b factor changes a forecastCalculate cumulative production from a decline curveWhy a decline forecast needs an end date and economic assumptionsExplore the same decline curve on monthly and annual time basesPreparing production data before a decline studySame first year different long term decline tailsWhy monthly rate samples do not exactly equal analytical cumulativeDecline curve teaching dataset and worked answer pack

Calculation sequence

  1. Choose an initial rate and a nominal decline per day on the same time basis as the horizon. A 10% effective annual decline is not an input of 0.10 per day.
  2. The engine selects the exponential equation for b = 0, harmonic for b = 1, and the hyperbolic relationship between those endpoints. The table samples 25 evenly spaced times, including zero and the horizon.
  3. Cumulative production is the analytical integral of the selected curve from zero to the horizon, not a sum of the sampled table rows. Compare a fitted curve with observed production before adopting its forecast.

Worked check

For q_i = 1,000 STB/day, D_i = 0.001/day and 365 days, b = 0 gives 694.197 STB/day and 305,803.349 STB. At b = 0.5, the endpoint rate is 715.150919 STB/day and cumulative is 308,668.076 STB. At time zero the rate is q_i and cumulative is zero.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

  • A parameter-driven, single-segment forecast, not an automatic history match or reserve estimate. No economic cutoff, downtime or operating change is included.
  • Use Arps assumptions appropriate to boundary-dominated decline. Transient unconventional behavior can require a different model or a modified decline segment.
  • Only 0 <= b <= 1 is supported. Values extremely close to endpoints are rejected unless the endpoint is selected, to avoid numerical cancellation. No infinite-time EUR is claimed.

Implemented equations

Arps Exponential Decline Rate

q(t)=qie−Ditq(t)=q_i e^{-D_i t}

Arps Exponential Decline Cumulative Production

Np(t)=qiDi(1−e−Dit)N_p(t)=\frac{q_i}{D_i}\left(1-e^{-D_i t}\right)

Arps Hyperbolic Decline Rate

q(t)=qi(1+bDit)1/bq(t)=\frac{q_i}{(1+bD_it)^{1/b}}

Arps Hyperbolic Decline Cumulative Production

Np(t)=qi(1−b)Di[1−(1+bDit)1−1/b]N_p(t)=\frac{q_i}{(1-b)D_i}\left[1-(1+bD_it)^{1-1/b}\right]

Arps Harmonic Decline Rate

q(t)=qi1+Ditq(t)=\frac{q_i}{1+D_it}

Arps Harmonic Decline Cumulative Production

Np(t)=qiDiln⁡(1+Dit)N_p(t)=\frac{q_i}{D_i}\ln(1+D_it)

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: . This does not claim independent expert review.

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