Decline curve teaching dataset and worked answer pack
PetroCalcHub · Original synthetic teaching exercise · 2026-10-24

Use this synthetic decline dataset to practice rate evaluation, cumulative integration and time-basis checks. The values are generated from stated parameters and are not production observations.

Exponential qi = 1,000 STB/day, nominal D = 0.001/day. The finite elapsed duration varies.

1. Why is this exact dataset unsuitable as evidence of a model's field prediction accuracy?

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2. Reproduce the baseline Analytical cumulative (STB) without rounding intermediate values.

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3. Compare the first and last recorded scenarios. Which input changes?

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4. What would be needed to apply this example to a different physical system?

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5. Convert 20% effective annual exponential decline to nominal annual decline.

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6. For monotonically decreasing rate, which endpoint rectangle sum overstates cumulative?

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ANSWER KEY

1. It was generated by the same stated curve. Recovering it verifies arithmetic, not predictive performance on independent observations.
2. Np(365) = 1,000[1 − exp(−0.365)]/0.001; endpoint rectangle = [1,000 exp(−0.365)] × 365. Analytical cumulative (STB) = 305803.349. The endpoint rectangle misses earlier higher rates. The analytical cumulative remains conditional on the finite horizon.
3. Elapsed time (day) changes from 30 to 1825. Other controls remain as stated in the premise. Analytical cumulative (STB) changes from 29554.4665 to 838782.356.
4. Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. t in days gives rate in STB/day and cumulative in STB. Endpoint rectangle q(t)t is shown only as a deliberately approximate comparison. The endpoint rectangle misses earlier higher rates. The analytical cumulative remains conditional on the finite horizon.
5. D = −ln(0.8) = 0.223143551/year. On a 365-day year, D = 0.000611352/day.
6. The left-endpoint sum overstates it; the right-endpoint sum understates it. State interval widths and sampling convention.

Method: Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Sources:
Equinor AutoDCA: decline equations, integrals and preprocessing: https://equinor.github.io/decline-curve-analysis/dca_report.html
Whitson: decline models, nominal decline and terminal switches: https://manual.whitson.com/modules/well-performance/decline-curve-analysis/