Power-Law Exponential Decline Calculator
Calculate power-law exponential oil decline rate using fitted coefficients. Keep time in days and distinguish D_hat from terminal nominal decline.
Calculate power-law exponential oil decline rate using fitted coefficients. Keep time in days and distinguish D_hat from terminal nominal decline.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Calculate a power-law exponential oil rate using a fitted amplitude, terminal decline coefficient, power-law coefficient and exponent. Unlike the stretched exponential form alone, this expression includes a separate terminal exponential term.
Evaluate a supplied PLE parameter set on a consistent daily time basis. Use the result to reproduce a forecast point or test parameter sensitivity, while keeping curve fitting and the justification for extrapolation separate from rate evaluation.
Solves for
q_t (STB/day)
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Formula, variables, and sourceReproduce the two exponent terms
For q_i = 1,000 STB/day, D_inf = 0.0005 per day, D_hat = 0.05 day^(-0.5), n = 0.5 and t = 365 days, the terminal term is 0.1825 and the power-law term is approximately 0.95524866. Applying their negative sum gives 320.539855 STB/day.
Setting D_inf to zero leaves a stretched exponential relation with D_hat = tau^(-n). Setting n to one gives an exponential decline coefficient D_inf + D_hat. These limiting checks distinguish the model's coefficients without claiming that any particular default represents a real well.
Rescale a time basis deliberately
If one new time unit contains c days, replace t_days by c times t_new, D_inf,new by c times D_inf,days and D_hat,new by c^n times D_hat,days. Both contributions to the exponential argument then remain unchanged. Only changing the elapsed-time entry changes the forecast incorrectly.
The published implementation deliberately labels the daily power-law coefficient day^(-n), rather than offering a fixed conversion factor for that input. The conversion depends on the exponent. Retain the fit's coefficient definitions and time origin when comparing results with another decline-analysis package.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns q_t = 320.539855 STB/day. Defaults demonstrate the implementation; they are not recommended field values.
1000
0.0005
0.05
0.5
365
Input definitions
q_i
STB/dayFitted Rate at the Model Time Origin
D_inf
1/dayTerminal Nominal Decline Coefficient
D_hat
day^(-n)Power-Law Coefficient (Units Depend on n)
n
dimensionlessPower-Law 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
Evaluate a supplied PLE parameter set on a consistent daily time basis. Use the result to reproduce a forecast point or test parameter sensitivity, while keeping curve fitting and the justification for extrapolation separate from rate evaluation.
Assumptions
- Nonnegative decline coefficients and 0 < n <= 1 describe the selected fitted production segment.
- Elapsed time is measured from the parameter set's time origin, with a consistent daily coefficient basis.
Limitations
- This calculator does not fit a curve, integrate production or certify a reserves estimate.
- The equation does not model a future change in pressure, artificial lift, operating constraints or completion.
Common mistakes
- Assigning 1/day units to D_hat regardless of n; its units are day^(-n).
- Changing the time basis without rescaling both coefficients, or confusing D_hat with instantaneous initial decline.
Frequently asked questions
What inputs does the Power-Law Exponential Decline Rate calculator need?
The calculation uses Fitted Rate at the Model Time Origin (q_i), Terminal Nominal Decline Coefficient (D_inf), Power-Law Coefficient (Units Depend on n) (D_hat), Power-Law 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. This calculator does not fit a curve, integrate production or certify a reserves estimate. Assigning 1/day units to D_hat regardless of n; its units are day^(-n).
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, power-law exponential relation. D_hat has time^(-n) units to keep the exponent dimensionless.
Open source reference