Calculator Inputs
Example Data Table
Illustrative example showing how an Arps forecast may be documented for a single well study.
| Well | Model | qi | Di | b | Forecast Years | Economic Limit | End Rate | Cumulative |
|---|---|---|---|---|---|---|---|---|
| Well-A1 | Hyperbolic | 1,200 bbl/day | 18%/year | 0.75 | 10 | 120 bbl/day | 368.88 bbl/day | 2,313,626.24 bbl |
| Well-B3 | Exponential | 800 bbl/day | 15%/year | 0.00 | 5 | 200 bbl/day | 377.89 bbl/day | 1,026,475.12 bbl |
| Well-C7 | Harmonic | 950 mcf/day | 22%/year | 1.00 | 8 | 150 mcf/day | 344.20 mcf/day | 2,677,858.51 mcf |
Formula Used
1) Exponential Decline
q(t) = qi × e-Dit
Np(t) = days × (qi - q(t)) / Di
2) Hyperbolic Decline
q(t) = qi / (1 + bDit)1/b
Np(t) = days × [qi / ((1-b)Di)] × [1 - (q/qi)1-b]
3) Harmonic Decline
q(t) = qi / (1 + Dit)
Np(t) = days × (qi / Di) × ln(qi / q)
In these equations, q(t) is rate at time t, qi is initial rate, Di is nominal initial decline, b is the hyperbolic exponent, and Np is cumulative production. The calculator also estimates time to the chosen economic rate limit.
How to Use This Calculator
- Enter a well or asset name for the scenario.
- Select exponential, hyperbolic, or harmonic decline behavior.
- Provide the initial production rate and nominal annual decline.
- Enter a b-factor when using hyperbolic decline.
- Set the forecast length and reporting time step.
- Define the economic limit rate and operating day basis.
- Choose rate and cumulative units for clean reporting.
- Click Calculate Decline Forecast to generate results, graph, and forecast table.
- Use the CSV button for spreadsheet review or the PDF button for report sharing.
Frequently Asked Questions
1) What does the Arps decline model estimate?
It estimates how production rate changes with time after a well begins declining. It also helps forecast cumulative production, future rate, and approximate remaining recoverable reserves under a chosen decline behavior.
2) When should I use exponential decline?
Use exponential decline when the decline percentage stays constant with time. It often fits late-life wells and provides a conservative, stable projection compared with stronger curvature in hyperbolic forecasts.
3) What is the meaning of the b-factor?
The b-factor controls forecast curvature in hyperbolic decline. Lower values behave closer to exponential decline, while higher values keep rates elevated longer and can materially increase cumulative production estimates.
4) Why is the economic limit rate important?
The economic limit rate marks the point where production may no longer justify operating costs. Time to that limit helps compare projects, schedule workovers, and estimate practical recovery rather than purely technical recovery.
5) Does cumulative production depend on days per year?
Yes. The cumulative calculation integrates rate over time, so the operating day basis matters. A value of 365 assumes continuous production, while lower values can reflect downtime or planned operating constraints.
6) Can this calculator be used for gas wells?
Yes. The mathematics are unit-agnostic. You can enter gas rates, oil rates, or other throughput units, provided the rate unit and cumulative unit remain internally consistent throughout the forecast.
7) Why does harmonic decline often predict higher recovery?
Harmonic decline reduces the rate more slowly than exponential decline at later times. That slower tail can increase long-range cumulative production, especially when the forecast horizon is long.
8) Should I rely on one decline model only?
Usually no. Engineers commonly compare several models, history-match the forecast, and test sensitivities. Using multiple scenarios can show upside, base, and downside recovery cases for planning decisions.