Stretched Exponential Decline Calculator
Calculate stretched exponential oil rate from fitted initial rate, characteristic time and exponent. Check the time basis and model limitations.
Calculate stretched exponential oil rate from fitted initial rate, characteristic time and exponent. Check the time basis and model limitations.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate a stretched exponential production-rate curve from its fitted initial rate, characteristic time and exponent. This calculator adds a distinct time-rate model to the Arps family; it does not fit production history or estimate recoverable reserves.
Use a previously fitted parameter set to reproduce a rate at a selected elapsed time or compare forecast sensitivity. The elapsed time and characteristic time must both be in days, and the time origin must match the history used for fitting.
Solves for
q_t (STB/day)
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Formula, variables, and sourceCheck the characteristic time
With a fitted oil rate of 1,000 STB/day, tau = 365 days, n = 0.5 and t = 365 days, the dimensionless ratio t/tau is one. The exponential argument is therefore -1 and the calculated rate is 367.879441 STB/day. This is a synthetic check, not a fitted well history.
At t = 0 the rate is 1,000 STB/day. At t = 4 tau the square-root exponent gives exp(-2), or 135.335283 STB/day. When n = 1, the model becomes ordinary exponential decline with nominal decline coefficient 1/tau.
| Elapsed time (day) | Oil rate (STB/day) |
|---|---|
| 0 | 1,000 |
| 365 | 367.879441 |
| 1,460 | 135.335283 |
A rate evaluator is not a history match
Separate a model's arithmetic from its suitability for a reservoir. Before extending a fitted curve, review the production interval, shut-ins, rate constraints and changes in completion or operating conditions. A smooth forecast is not evidence that those future conditions will remain unchanged.
The initial-rate inverse recovers the fitted amplitude for a supplied rate and the same tau, n and t. It cannot infer all three parameters from one test point. For n below one, the rate remains finite at the origin even though its instantaneous decline derivative is singular there; this page evaluates rate, not that derivative.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns q_t = 367.879441 STB/day. Defaults demonstrate the implementation; they are not recommended field values.
1000
365
0.5
365
Input definitions
q_i
STB/dayFitted Rate at the Model Time Origin
tau
dayCharacteristic Decline Time
n
dimensionlessStretched Exponential Exponent (0 < n <= 1)
t
dayElapsed Time from the Fitted Origin
Output definitions
q_t
Oil Rate at Elapsed Time
q_i
Fitted Rate at the Model Time Origin
Engineering use, assumptions, and limits
Use a previously fitted parameter set to reproduce a rate at a selected elapsed time or compare forecast sensitivity. The elapsed time and characteristic time must both be in days, and the time origin must match the history used for fitting.
Assumptions
- The fitted parameters and time origin describe the same production-history segment.
- Characteristic time is positive and the implemented stretched range is 0 < n <= 1.
Limitations
- No production-data fitting, cumulative integration, economic cutoff or EUR calculation is performed.
- An empirical rate curve does not establish a flow regime or account for future operating changes.
Common mistakes
- Treating the fitted initial-rate parameter as a measured peak rate without checking the time origin.
- Entering months for t while tau remains in days, or treating n as an Arps b-factor.
Frequently asked questions
What inputs does the Stretched Exponential Decline Rate calculator need?
The calculation uses Fitted Rate at the Model Time Origin (q_i), Characteristic Decline Time (tau), Stretched Exponential Exponent (0 < n <= 1) (n), Elapsed Time from the Fitted Origin (t). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is oil rate at elapsed time in STB/day. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. No production-data fitting, cumulative integration, economic cutoff or EUR calculation is performed. Treating the fitted initial-rate parameter as a measured peak rate without checking the time origin.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
Decline-Curve Analysis for Gas Wells, T. A. Blasingame (2016)
T. A. Blasingame, Texas A&M P613 Lecture 8: Decline-Curve Analysis for Gas Wells (2016), slide 34, stretched exponential relation. Oil-rate units selected here; the rate relation is homogeneous in rate.
Open source reference