reservoir · decline analysis
Hyperbolic Decline
q(t) = qi / (1 + b·Di·t)^(1/b)
click formula to derive ↑
Inputs
STB/d
frac/yr
—
years
STB/d
Description
Projects production rate using the general Arps hyperbolic decline model and estimates EUR to a specified economic limit rate. The hyperbolic model is the standard decline form for unconventional wells, with the b-factor controlling how quickly the decline rate itself decays over time.
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 initial decline rate from a type-curve or rate-time fit. |
| b | — | Arps hyperbolic exponent. b=0 is exponential, b=1 is harmonic, 0<b<1 is typical conventional hyperbolic, b>1 often signals transient (not boundary-dominated) flow. |
| 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 (independent of the forecast time t). |
Assumptions
- qi, Di, and b were fit to representative boundary-dominated-flow production data, with early transient/flush production excluded where possible
- The decline parameters remain constant over the period being forecast — no future workovers, artificial lift changes, or facility constraints
- The economic limit rate qa reflects current and expected future operating costs and prices, not an arbitrary cutoff
Limitations
- b-factors greater than 1 are mathematically permitted by this equation but physically indicate transient (not boundary-dominated) flow, where decline curve EUR projections are unreliable and tend to overstate reserves
- A single b value applied indefinitely does not capture wells that transition between flow regimes — many practitioners switch to exponential decline at late time (a "modified hyperbolic")
- Very low qa values can produce unrealistically large EUR for b close to or above 1 — sense-check against analog well performance
Use Cases
- → Unconventional well EUR forecasting: Forecast remaining recoverable volume for shale/tight wells exhibiting hyperbolic decline behavior, using a b-factor fit from production history.
- → Type curve construction: Build representative type curves for undrilled locations using analog qi, Di, and b parameters from offset wells in the same bench.
- → Reserve category support: Support PUD/probable reserve bookings with a defensible decline-curve EUR, cross-checked against volumetric GIIP/OOIP.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring horizontal wells commonly show b=0.8-1.3 in the first 1-2 years, declining toward b=0.3-0.6 at late time; first-year Di of 60-80%/yr is typical.
Eagle Ford
Mature wells often show b=0.9-1.5 early, transitioning to a modified-exponential late-time trend (D≈10-20%/yr) after 5-7 years.
Bakken
Middle Bakken/Three Forks wells typically exhibit b=1.0-1.8 during the first 12-18 months due to extended transient linear flow in the stimulated rock volume.
Haynesville
High-rate shale gas wells often show b>1 (sometimes 1.5-2.0) during early time; analysts frequently cap b at 1.0-1.2 for reserves purposes to avoid overstating EUR.
References
Primary source
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