Engineering lesson
Explore the same decline curve on monthly and annual time bases
The same exponential curve can be expressed per day, month or year if nominal decline and elapsed time are transformed together. The dimensionless product Dt must remain unchanged.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Convert the coefficient and the axis together
A nominal decline of 0.365/year is 0.001/day on a 365-day year. At one year, exp(−0.365) is identical to exp(−0.001 × 365).
An assumed month length must be stated. Twelve equal model months and actual calendar months are different time discretizations.
Effective decline is another quantity
The effective decline over one interval is 1 − exp(−DΔt). It cannot be obtained merely by relabelling a nominal annual coefficient as a monthly percentage.
The explorer changes the displayed time basis while retaining the same physical elapsed time and daily-rate unit. The endpoint rate should therefore be invariant.
Keep the cumulative unit conversion
A rate in STB/day integrated against an axis expressed in years requires a days-per-year multiplier. Changing the axis label alone can create a factor-of-365 cumulative error.
The data table preserves physical elapsed days alongside the alternate basis to make this check visible.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 4 recorded scenarios. Intermediate states are not interpolated.
Days per display unit = 30.4166667. Nominal D (1/display unit): 0.0304166667; Elapsed display units: 12; Endpoint rate (STB/day): 694.196651.
- Nominal D (1/display unit)
Worked example
One exponential curve on equivalent time bases
Physical elapsed time 365 days, qi = 1,000 STB/day and D = 0.001/day. A model year is 365 days and a model month is one twelfth of it.
Relation and unit basis
Dnew = Dday × days per unit; tnew = 365/(days per unit)
The time basis changes, while Dt and the physical rate remain invariant. The first column is days per display unit.
1. Define the baseline
Days per display unit = 30.4166667
Physical elapsed time 365 days, qi = 1,000 STB/day and D = 0.001/day. A model year is 365 days and a model month is one twelfth of it.
2. Select the relation
Dnew = Dday × days per unit; tnew = 365/(days per unit)
The time basis changes, while Dt and the physical rate remain invariant. The first column is days per display unit.
3. Substitute the values
Dmonth = 0.001 × 365/12; t = 12 months; Dmonth × 12 = 0.365; q = 1,000 exp(−0.365)
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Nominal D (1/display unit) = 0.0304166667; Elapsed display units = 12; Endpoint rate (STB/day) = 694.196651
Changing axis units together with the coefficient must not change the physical endpoint rate.
Result and interpretation
Nominal D (1/display unit) = 0.0304166667; Elapsed display units = 12; Endpoint rate (STB/day) = 694.196651
Changing axis units together with the coefficient must not change the physical endpoint rate.
The rows represent equivalent parameterizations, not different reservoir forecasts.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Days per display unit | Nominal D (1/display unit) | Elapsed display units | Endpoint rate (STB/day) |
|---|---|---|---|
| 1 | 0.001 | 365 | 694.1967 |
| 7 | 0.007 | 52.14286 | 694.1967 |
| 30.41667 | 0.03041667 | 12 | 694.1967 |
| 365 | 0.365 | 1 | 694.1967 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. What nominal monthly decline matches 0.365/year if a model year has twelve equal months?
Show the worked answer
0.365/12 = 0.0304166667 per model month. At twelve months, Dt remains 0.365.
2. Reproduce the baseline Nominal D (1/display unit) without rounding intermediate values.
Show the worked answer
Dmonth = 0.001 × 365/12; t = 12 months; Dmonth × 12 = 0.365; q = 1,000 exp(−0.365). Nominal D (1/display unit) = 0.0304166667. Changing axis units together with the coefficient must not change the physical endpoint rate.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Days per display unit changes from 1 to 365. Other controls remain as stated in the premise. Nominal D (1/display unit) changes from 0.001 to 0.365.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. The time basis changes, while Dt and the physical rate remain invariant. The first column is days per display unit. Changing axis units together with the coefficient must not change the physical endpoint rate.
Before using the result
- Preserve Dt.
- State the month and year conventions.
- Convert integration time as well as decline.
Changing axis units together with the coefficient must not change the physical endpoint rate.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.