Logistic Cumulative Oil Production Calculator
Calculate logistic cumulative oil production from fitted asymptote, half-production time and exponent. The asymptote is not a certified reserves estimate.
Calculate logistic cumulative oil production from fitted asymptote, half-production time and exponent. The asymptote is not a certified reserves estimate.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Calculate cumulative oil production with the Clark-type logistic-growth relation using a fitted asymptote, half-production time and positive exponent. The half-time parameter replaces the original coefficient a with t_half raised to n, making the time units explicit.
Enter a fitted cumulative asymptote in STB, the number of days needed to reach half that value, and the growth exponent. Use the result to reproduce a curve point or compare the linked derivative rate; do not interpret the fitted asymptote as independently established recoverable reserves.
Solves for
N_p (STB)
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Formula, variables, and sourceCheck the cumulative half-time
With K = 100,000 STB, t_half = 365 days and n = 2, cumulative production at day 365 is exactly K/2, or 50,000 STB. At day 730, the dimensionless time power is four and the result is 80,000 STB. At the model origin it is zero; as time tends to infinity it approaches K.
The source equation is Q = K t^n/(a + t^n). Substituting a = t_half^n gives the displayed expression without changing the model. A synthetic asymptote is used here only to check arithmetic; it is not production history or evidence that a well will recover 100,000 STB.
| Elapsed time (day) | Cumulative oil (STB) |
|---|---|
| 0 | 0 |
| 365 | 50,000 |
| 730 | 80,000 |
Check rate and cumulative together
Differentiating this cumulative expression gives the linked logistic production-rate formula. For the same parameters, the rate at day 365 is 136.986301 STB/day. Integrating that rate from the model origin reproduces cumulative production; using a rate curve with a different exponent or time origin breaks that consistency.
For n greater than one, cumulative production initially accelerates and its rate rises before declining. For n below one, cumulative production is still finite at the origin but its rate is singular there. These distinctions matter when deciding which part of a measured production history could plausibly be described by the fitted model.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns N_p = 50,000 STB. 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 Logistic Growth Exponent
t
dayElapsed Time from the Fitted Origin
Output definitions
N_p
Modeled Cumulative Oil Production
Engineering use, assumptions, and limits
Enter a fitted cumulative asymptote in STB, the number of days needed to reach half that value, and the growth exponent. Use the result to reproduce a curve point or compare the linked derivative rate; do not interpret the fitted asymptote as independently established recoverable reserves.
Assumptions
- A positive exponent and positive half-time define the same fitted empirical production curve.
- Cumulative production is measured from the model's zero-cumulative origin on a consistent stock-tank oil and daily time basis.
Limitations
- The evaluator does not infer parameters from production data, add pre-origin production or impose an economic limit.
- An asymptotic curve and bounded cumulative output do not establish reserves, reservoir physics or future operating conditions.
Common mistakes
- Entering the original a parameter in the half-time field; a has day^n units whereas t_half has day units.
- Using an ordinary exponential logistic sigmoid instead of this time-power relation, or adding already-produced oil twice.
Frequently asked questions
What inputs does the Logistic Growth Cumulative Oil Production calculator need?
The calculation uses Fitted Cumulative Asymptote (Not Verified Reserves) (K), Time to Half of the Fitted Asymptote (t_half), Positive Logistic Growth Exponent (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 cumulative oil production in STB. 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. The evaluator does not infer parameters from production data, add pre-origin production or impose an economic limit. Entering the original a parameter in the half-time field; a has day^n units whereas t_half has day units.
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.
Patrick Collins, Texas A&M University master's thesis (2016), Appendix E, printed page 141 (PDF page 152), equation E.1: Q = K t^n / (a + t^n). Here a = t_half^n is an explicit half-time reparameterization.
Open source reference