Modified Hyperbolic Decline Calculator
Calculate modified hyperbolic oil rate with a continuous terminal exponential switch. Use daily nominal decline coefficients, not effective percentages.
Calculate modified hyperbolic oil rate with a continuous terminal exponential switch. Use daily nominal decline coefficients, not effective percentages.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate an oil-rate curve that starts with hyperbolic decline and switches to terminal exponential decline when its nominal decline reaches the selected terminal coefficient. The transition preserves both rate and its time derivative, rather than splicing two unrelated forecasts.
Supply a previously fitted initial rate, initial nominal decline and positive b-factor, then specify a terminal nominal decline no larger than the initial value. All times and decline coefficients use a daily basis. This evaluates a forecast point, not a production-history fit.
Solves for
q_t (STB/day)
Best next page
Formula, variables, and sourceCheck the continuous terminal switch
For q_i = 1,000 STB/day, D_i = 0.002 per day, D_t = 0.0005 per day and b = 0.8, the switch time is 1,875 days. Hyperbolic nominal decline D_i/(1 + b D_i t) equals D_t there. The switch rate is 176.776695 STB/day; 625 more days of exponential decline gives 129.332593 STB/day at day 2,500.
At the switch, both branches have derivative -D_t times the switch rate. This matching prevents a rate or slope discontinuity. The formula displayed above uses t_h = min(t, t_s) to write the same two-branch relation compactly; the intermediate results expose the switch time and hyperbolic duration.
| Elapsed time (day) | Oil rate (STB/day) |
|---|---|
| 0 | 1,000 |
| 1,875 | 176.776695 |
| 2,500 | 129.332593 |
Keep nominal decline and forecast scope distinct
For an exponential segment over a period Delta t, effective decline is 1 - exp(-D Delta t). That is not the nominal coefficient D itself. Convert annual or monthly coefficients to the daily basis before entering them, and do not reinterpret a quoted percentage without first checking its definition.
When D_t equals D_i, the switch occurs at the origin and the model is exponential from the start. This calculator requires b greater than zero; its small-b rate approaches the exponential limit, while the linked Arps decline workflow handles ordinary exponential cases directly. That workflow is a separate Arps forecast, not a modified-hyperbolic fitting tool.
Compare compatible calculations
Arps Decline Curve Forecast CalculatorLearn, 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 = 129.332593 STB/day. Defaults demonstrate the implementation; they are not recommended field values.
1000
0.002
0.0005
0.8
2500
Input definitions
q_i
STB/dayFitted Oil Rate at the Model Origin
D_i
1/dayInitial Nominal Decline Coefficient
D_t
1/dayTerminal Nominal Decline (0 < D_t <= D_i)
b
dimensionlessPositive Hyperbolic Decline Exponent
t
dayElapsed Time from the Fitted Origin
Output definitions
q_t
Oil Rate at Elapsed Time
Engineering use, assumptions, and limits
Supply a previously fitted initial rate, initial nominal decline and positive b-factor, then specify a terminal nominal decline no larger than the initial value. All times and decline coefficients use a daily basis. This evaluates a forecast point, not a production-history fit.
Assumptions
- The fitted hyperbolic parameters and time origin refer to the same production interval.
- Initial and terminal nominal decline are positive, terminal decline does not exceed initial decline, and b is positive.
Limitations
- No history matching, cumulative integration, operating constraint, economic cutoff or reserves certification is performed.
- Choosing a terminal decline does not establish when the well actually reaches boundary-dominated flow or validate an empirical extrapolation.
Common mistakes
- Entering an annual effective decline percentage as a daily nominal coefficient without converting its definition and time basis.
- Continuing hyperbolic decline after the chosen switch, or using an exponential amplitude that does not match the switch rate.
Frequently asked questions
What inputs does the Modified Hyperbolic Decline Rate calculator need?
The calculation uses Fitted Oil Rate at the Model Origin (q_i), Initial Nominal Decline Coefficient (D_i), Terminal Nominal Decline (0 < D_t <= D_i) (D_t), Positive Hyperbolic Decline Exponent (b), 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 history matching, cumulative integration, operating constraint, economic cutoff or reserves certification is performed. Entering an annual effective decline percentage as a daily nominal coefficient without converting its definition and time 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.
2017 SPE GCS Reservoir Forum presentation, T. A. Blasingame (2017)
T. A. Blasingame, 2017 SPE Gulf Coast Section Reservoir Forum, slide 27: modified hyperbolic decline, terminal rate and switch time. The capped-time expression here is algebraically equivalent to the published piecewise relation.
Open source reference