reservoir · decline analysis
Harmonic Decline
q(t) = qi / (1 + Di·t)
click formula to derive ↑
Inputs
STB/d
frac/yr
years
STB/d
Description
Projects production rate using the harmonic decline model — the special case of Arps hyperbolic decline at b=1 — and estimates EUR to a specified economic limit rate. Harmonic decline produces the slowest rate of decline-rate decay among the Arps family and is most appropriate for some water-drive or gravity-drainage reservoirs.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q(t) | STB/d | Rate at Time t |
| EUR | STB | EUR to Economic Limit |
| qi | STB/d | Initial production rate at the start of the decline period. |
| Di | frac/yr | Nominal decline rate from a rate-time fit, used in the harmonic (b=1) form. |
| t | years | Forecast time at which to evaluate the rate q(t). |
| qa | STB/d | Rate at which the well becomes uneconomic — used to compute EUR to depletion. |
Assumptions
- qi and Di were fit to production data that genuinely follows a harmonic (b=1) trend, not assumed by default
- The decline rate Di remains constant over the period being forecast
- The economic limit rate qa is set appropriately for current operating economics
Limitations
- True harmonic decline (b exactly 1) is relatively uncommon — verify with a diagnostic plot (log q vs. t) before assuming b=1 rather than fitting a general hyperbolic model
- Harmonic decline produces the largest EUR of the three Arps models for a given qi and Di — using it by default without justification will overstate reserves
- Like all Arps models, harmonic decline assumes boundary-dominated flow; applying it to transient-flow data is invalid
Use Cases
- → Water-drive reservoir EUR: Apply harmonic decline to wells in strong water-drive reservoirs where production history shows a slowly flattening decline rate consistent with b≈1.
- → Decline model comparison: Run harmonic alongside exponential and general hyperbolic decline on the same data to bound EUR uncertainty from decline-model choice alone.
- → Late-life reserve forecasting: Forecast remaining life and EUR for mature wells where the harmonic trend has been validated against several years of production history.
Related Calculations
Region Notes
Gulf of Mexico
Some mature, strongly water-driven Miocene reservoirs show late-life decline trends approaching harmonic (b≈0.9-1.0) as water drive sustains rates longer than exponential decline would predict.
Permian Basin
Harmonic decline is rarely appropriate for Wolfcamp/Bone Spring unconventional wells, which are depletion-drive and better fit by hyperbolic b<1 at late time — use with caution here.
North Sea
Gravity-drainage-dominated fields (e.g., some Brent Group accumulations under gas cap expansion) have occasionally shown near-harmonic late-time decline.
Global
Always plot the decline-rate-vs-time diagnostic (D vs t on log-log) to confirm b≈1 before committing to the harmonic model over the more general hyperbolic fit.
References
Primary source
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