reservoir · decline analysis
Estimated Ultimate Recovery (EUR) from Decline Parameters
EUR = f(qi, Di, b, qa) for exponential, hyperbolic, and harmonic decline
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Inputs
STB/d
frac/yr
—
STB/d
Description
Computes EUR to a common economic limit rate under all three Arps decline assumptions — exponential, hyperbolic, and harmonic — side by side from the same qi, Di, b, and qa inputs. Comparing the three highlights how sensitive reserves estimates are to the choice of decline model. The economic limit rate (qa) is an input here, not derived — use the Economic Limit Rate calculator (Economics) to compute qa from oil price, net revenue interest, and operating cost rather than assuming a value.
Variables
| Symbol | Unit | Description |
|---|---|---|
| EURexp | STB | EUR (Exponential, b=0) |
| EURhyp | STB | EUR (Hyperbolic) |
| EURhar | STB | EUR (Harmonic, b=1) |
| qi | STB/d | Initial production rate at the start of the decline period. |
| Di | frac/yr | Nominal initial decline rate, applied consistently across all three decline-type EUR calculations for direct comparison. |
| b | — | Arps hyperbolic exponent used only in the hyperbolic EUR calculation, shown alongside the exponential (b=0) and harmonic (b=1) cases for comparison. |
| qa | STB/d | Rate at which the well becomes uneconomic, used as the depletion endpoint for all three EUR calculations. |
Assumptions
- The same qi, Di, and qa are valid starting points for comparing all three decline models, even though only one model will ultimately be selected as representative
- b is only used in the hyperbolic calculation but is specified consistently with the well's actual production behavior where known
- All three EURs represent depletion to the same economic limit rate, not a fixed forecast time
Limitations
- This comparison does not by itself indicate which decline model is correct for the well — that determination requires fitting actual production history
- A large spread between EUR_exp and EUR_har indicates high decline-model uncertainty, which single-model reserves bookings can understate
- Does not capture multi-segment decline (e.g., transient hyperbolic transitioning to late-time exponential), which often fits real production data better than any single Arps model
Use Cases
- → Reserves uncertainty bounding: Use the spread between EUR_exp, EUR_hyp, and EUR_har as a quick proxy for decline-model uncertainty in a reserves range estimate.
- → Model selection sanity check: Compare against an independently fitted decline model to confirm the chosen b-factor is not producing an outlier EUR relative to the other two cases.
- → Type curve QC: Cross-check type curve EUR assumptions used in economic models against all three Arps cases before finalizing development economics.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring type curves commonly show EUR_hyp 1.5-2.5× EUR_exp for the same qi/Di when b=0.8-1.2 is used, highlighting material model sensitivity for unconventional reserves bookings.
Eagle Ford
For wells already transitioned to late-time exponential decline, EUR_exp and EUR_hyp converge closely, signaling the hyperbolic b-factor is no longer materially affecting the forecast.
Bakken
Early-time high-b wells (b>1.3) can show EUR_har more than 3× EUR_exp — a useful trigger for the warn flag and a prompt to cap b for reserves purposes.
Global
Operators commonly report a "decline model sensitivity" case in reserves documentation — this calculator directly produces that comparison.
References
Primary source
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