reservoir · decline analysis
Exponential Decline
q(t) = qi × e^(−D×t)
click formula to derive ↑
Inputs
STB/d
frac/yr
years
Description
Projects production rate forward in time using the exponential (Arps b=0) decline model and estimates cumulative production (EUR) over the forecast period. The simplest and most conservative of the Arps decline models.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q(t) | STB/d | Rate at Time t |
| qi | STB/d | Initial production rate at the start of the decline period (t=0), typically the peak or post-cleanup stabilized rate. |
| D | frac/yr | Nominal (continuous) exponential decline rate, derived from a semi-log plot of historical production rate vs. time. |
| t | years | Length of the forecast period over which to project the rate and cumulative production (EUR). |
Assumptions
- The decline rate D is constant over the forecast period — no new completions, workovers, or artificial lift changes that would alter the decline trend
- qi and D were fit to representative production data with transient/flush production excluded
- The well will continue producing to the forecast time t without facility constraints (e.g., compression, gathering pressure) limiting the rate
Limitations
- Exponential decline systematically underestimates EUR for unconventional wells, which typically follow hyperbolic or stretched-exponential trends with b>0
- A single D value cannot capture changes in decline behavior across flow regimes (transient, transition, boundary-dominated)
- Extrapolating far beyond the history-matched period increases uncertainty substantially — always compare against analog wells in the same play
Use Cases
- → EUR estimation: Estimate remaining recoverable volume over a defined forecast horizon for a well or type curve.
- → PDP reserve booking: Support proved developed producing (PDP) reserve estimates using a conservative exponential decline assumption.
- → Cash flow forecasting: Generate a rate forecast as the production input to an economic cash flow model.
Related Calculations
Region Notes
Permian Basin
Unconventional Wolfcamp/Bone Spring wells typically follow hyperbolic decline with b=0.8-1.2 and first-year nominal decline rates of 60-80%/yr — exponential decline should only be applied to late-time data once b approaches 0.
Eagle Ford
Mature Eagle Ford wells often transition to exponential decline (D≈10-20%/yr) after 5-7 years on production, once the hyperbolic b-factor has flattened.
Gulf of Mexico
Conventional GOM shelf and deepwater reservoirs commonly follow exponential decline with D in the range of 10-25%/yr for boundary-dominated flow.
References
Primary source
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