reservoir · decline analysis
Nominal Decline Rate (from Two Points)
D = ln(q1/q2) / (t2−t1) [exponential]
click formula to derive ↑
Inputs
STB/d
years
STB/d
years
—
Description
Back-calculates the nominal (continuous) Arps decline rate D from two production rate observations at known times, optionally assuming a hyperbolic b-factor. This is the standard way to derive D directly from field data before forecasting with the exponential, hyperbolic, or harmonic decline calculators.
Variables
| Symbol | Unit | Description |
|---|---|---|
| D | frac/yr | Nominal Decline Rate |
| Deff | frac/yr | Effective Decline Rate |
| q1 | STB/d | Production rate observed at the earlier time t1. |
| t1 | years | Time of the first rate observation, in years from a consistent reference point (e.g., first production). |
| q2 | STB/d | Production rate observed at the later time t2. |
| t2 | years | Time of the second rate observation, in years from the same reference point as t1. |
| b | — | Arps b-factor to assume when back-calculating D. Leave at 0 for the simple exponential form; set to a fitted value to back-calculate D for a hyperbolic trend. |
Assumptions
- Both rate observations come from the same well (or type-curve composite) and the same producing phase, free of mechanical or facility-driven rate changes
- The interval between t1 and t2 reflects boundary-dominated flow consistent with the assumed b-factor, not transient flow
- Rates are stabilized values, not transient flowback or post-workover spikes
Limitations
- A two-point calculation is sensitive to noise in either rate measurement — fitting a full regression line through multiple points is more robust where data permits
- Assuming b=0 (exponential) when the well is actually declining hyperbolically will understate the true decline rate and bias forecasts
- Step-changes in choke size, artificial lift, or facility constraints between t1 and t2 will bias the calculated D away from the true reservoir decline behavior
Use Cases
- → Quick D estimation from two production reports: Estimate a working decline rate from two known rate-time data points (e.g., two monthly production reports) without a full regression workflow.
- → Type curve parameter derivation: Derive representative D and Deff values from analog well production history to seed a type curve for an undrilled location.
- → Decline rate trend monitoring: Repeatedly apply this calculation across sequential time windows to track whether a well's decline rate is accelerating, stable, or flattening.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring horizontal wells often show first-year effective decline of 60-75%, dropping to 25-35%/yr by year 3 — track D over multiple windows rather than relying on a single two-point estimate.
Eagle Ford
Early-life D estimates (first 6 months) are frequently distorted by flowback and cleanup effects — prefer rate pairs from month 3 onward for a representative decline rate.
Bakken
Choke management programs intentionally suppress early rates to extend well life — D calculated across a choke-management period will understate the well's natural decline rate.
Global
Always verify that no workover, refrac, or artificial lift change occurred between t1 and t2 before trusting the calculated D as representative of natural reservoir decline.
References
Primary source
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