Logistic Oil Production Rate Calculator
Calculate logistic oil rate consistent with cumulative production. Check exponent-dependent origin behavior and the initial rising-rate branch before use.
Calculate logistic oil rate consistent with cumulative production. Check exponent-dependent origin behavior and the initial rising-rate branch before use.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate the derivative of a Clark-type logistic cumulative-production curve from its fitted asymptote, half-time and exponent. This is not necessarily a decline-only model: when the exponent exceeds one, rate first rises and subsequently declines.
Use the same K, half-production time, exponent and time origin as the cumulative calculator. Evaluate a supplied fitted curve point in STB/day and examine whether its rising or declining branch matches the interval being studied; the parameters are not fitted from one input point.
Texas A&M Collins thesis: cumulative relation and rate derivation, Appendix ESolves for
q_t (STB/day)
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Formula, variables, and sourceLocate the rate peak, not just the half-time
For K = 100,000 STB, t_half = 365 days and n = 2, the rate at day 365 is 136.986301 STB/day. The rate peak occurs earlier, at t_half/sqrt(3) = 210.732848 days, with 177.950425 STB/day. Half the cumulative asymptote is reached at day 365, not at the rate peak.
For a general n greater than one, differentiating the rate gives t_peak = t_half[(n - 1)/(n + 1)]^(1/n). That derivation applies only to the positive interior peak. For n at or below one there is no positive interior peak of this kind, so the same expression must not be applied blindly.
| Elapsed time (day) | Oil rate (STB/day) |
|---|---|
| 0 | 0 |
| 210.732848 | 177.950425 |
| 365 | 136.986301 |
| 730 | 43.835616 |
Handle the origin and the time basis
At zero time, n greater than one gives zero rate and n equal to one gives K/t_half. An exponent between zero and one gives a divergent rate even though cumulative production starts at zero. The calculator reports that singular origin as an input error instead of fabricating a finite rate.
If times are rescaled to a unit containing c days, both t and t_half must be divided by c; the numerical rate per new time unit becomes c times the daily rate. Cumulative production remains unchanged. The interface keeps a daily basis, while the regression suite checks that this unit transformation and the cumulative derivative agree.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns q_t = 136.986301 STB/day. Defaults demonstrate the implementation; they are not recommended field values.
100000
365
2
365
Input definitions
K
STBFitted Cumulative Asymptote (Not Verified Reserves)
t_half
dayTime to Half of the Fitted Asymptote
n
dimensionlessPositive Growth Exponent (Origin Singular Below 1)
t
dayElapsed Time from the Fitted Origin
Output definitions
q_t
Modeled Oil Production Rate
Engineering use, assumptions, and limits
Use the same K, half-production time, exponent and time origin as the cumulative calculator. Evaluate a supplied fitted curve point in STB/day and examine whether its rising or declining branch matches the interval being studied; the parameters are not fitted from one input point.
Assumptions
- The cumulative asymptote, half-time and exponent belong to one consistent empirical fit.
- Elapsed time and half-time use days, while the cumulative amplitude uses stock-tank barrels.
Limitations
- This is a rate evaluator, not a production-history regression, operational model or reserves estimate.
- For 0 < n < 1 the origin is singular and requires a positive elapsed time; a rising-rate branch must not be mistaken for monotonic decline.
Common mistakes
- Treating K in STB as an initial daily rate, or assuming t_half is the time of the rate peak.
- Evaluating zero time with n below one, or using parameters from a differently normalized cumulative curve.
Frequently asked questions
What inputs does the Logistic Growth Oil Production Rate calculator need?
The calculation uses Fitted Cumulative Asymptote (Not Verified Reserves) (K), Time to Half of the Fitted Asymptote (t_half), Positive Growth Exponent (Origin Singular Below 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 modeled oil production rate 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 is a rate evaluator, not a production-history regression, operational model or reserves estimate. Treating K in STB as an initial daily rate, or assuming t_half is the time of the rate peak.
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 (2016), slide 36: logistic-growth rate a K n t^(n-1)/(a+t^n)^2. The time parameter here is a = t_half^n.
Open source reference