Duong Oil Decline Rate Calculator
Calculate Duong oil rate from a fitted day-one rate and daily-basis coefficients. Check time normalization, the m = 1 limit and forecast applicability.
Calculate Duong oil rate from a fitted day-one rate and daily-basis coefficients. Check time normalization, the m = 1 limit and forecast applicability.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate the original Duong time-rate relation on its fixed one-day reference basis using a fitted day-one oil rate, ratio-rate coefficient and exponent. This adds a fracture-dominated empirical curve, not another Arps exponent setting or an automatically fitted production forecast.
Use a parameter set fitted with numerical elapsed time in days and a compatible production origin. Check the rate-to-cumulative log-log trend and operating conditions before extrapolating. The evaluator covers day one onward and excludes the optional additive terminal-rate extension.
Solves for
q_t (STB/day)
Best next page
Formula, variables, and sourceCheck the one-day rate anchor
Using the synthetic fit q_1 = 1,000 STB/day, a = 1.2 and m = 1.1 gives exactly 1,000 STB/day at day one. At day 10 the original power-and-exponential expression gives 937.271374 STB/day, and at day 365 it gives 319.217438 STB/day. These are arithmetic examples, not a history match for a real well.
The displayed x is elapsed time divided by one day. This normalization makes the exponential argument dimensionless and keeps the fitting convention explicit. In a dimensional rate-to-cumulative relation, the coefficient's units depend on m; copying its numerical value to a different time basis is not a valid conversion.
| Elapsed time (day) | Oil rate (STB/day) |
|---|---|
| 1 | 1,000 |
| 10 | 937.271374 |
| 365 | 319.217438 |
Inspect the limit and the rising-rate branch
As m approaches one, (x^(1-m) - 1)/(1-m) approaches ln(x). The rate therefore approaches q_1 x^(a-1), which is implemented as the continuous m = 1 limit. With a = 1.2 and m = 1, the day-365 value is 3,254.307394 STB/day: a rising curve, not evidence that production will increase indefinitely.
For m greater than one, setting the rate derivative to zero gives x_peak = (a/m)^(1/(m-1)). The default curve peaks near day 2.387182 at 1,043.807257 STB/day before declining. Some parameter choices put this peak before day one. Preserve the fitting interval and operating history; the calculator does not choose a terminal-flow model or approve an EUR estimate.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns q_t = 319.217438 STB/day. Defaults demonstrate the implementation; they are not recommended field values.
1000
1.2
1.1
365
Input definitions
q_1
STB/dayFitted Oil Rate at the One-Day Reference
a
dimensionlessPositive Ratio-Rate Coefficient on the One-Day Basis
m
dimensionlessPositive Duong Exponent (Not Arps b)
t
dayElapsed Time in Days (At or After Day One)
Output definitions
q_t
Modeled Oil Production Rate
Engineering use, assumptions, and limits
Use a parameter set fitted with numerical elapsed time in days and a compatible production origin. Check the rate-to-cumulative log-log trend and operating conditions before extrapolating. The evaluator covers day one onward and excludes the optional additive terminal-rate extension.
Assumptions
- The supplied coefficients belong to one fitted rate/cumulative history with a compatible time origin.
- Time is normalized by one day, a and m are positive, and the additive q_infinity offset is zero.
Limitations
- No fitting, pressure correction, cumulative integration, economic cutoff or recoverable-reserves certification is performed.
- The curve can rise initially or grow at late time for some parameters; a rate evaluator does not validate extrapolation or identify a flow regime.
Common mistakes
- Using months or years in the elapsed-time field with coefficients fitted on the one-day basis.
- Interpreting q_1 as a time-zero rate, peak rate or measured first-day average; it is the fitted rate at the reference time.
- Applying the curve without examining whether the rate-to-cumulative versus time log-log trend supports the model.
Frequently asked questions
What inputs does the Duong Oil Production Rate calculator need?
The calculation uses Fitted Oil Rate at the One-Day Reference (q_1), Positive Ratio-Rate Coefficient on the One-Day Basis (a), Positive Duong Exponent (Not Arps b) (m), Elapsed Time in Days (At or After Day One) (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. No fitting, pressure correction, cumulative integration, economic cutoff or recoverable-reserves certification is performed. Using months or years in the elapsed-time field with coefficients fitted on the one-day basis.
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.
Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs, Anh N. Duong (2011)
Anh N. Duong (2011), Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs, SPE Reservoir Evaluation & Engineering, 14(3), 377-387, equation 5, page 378, and Appendix A. Original rate relation without the later additive q_infinity extension; oil-rate specialization is homogeneous in rate.
Open source reference