Original synthetic study
The same wellbore with three synthetic thermal histories
This synthetic study compares the same thermal system under different shut-in durations. The different restart states come from stored formation heat, not a change in current material properties.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Define the schedule controls
The study fixes formation conductivity, heat capacity, geometry, heat-transfer coupling, initial temperature, heating duration and restart duration. Only the intermediate shut-in period changes.
Each scenario is solved by the site's thermal-history engine and retains its complete input schedule in the downloadable record.
Compare states at the same process milestone
Read restart-end temperatures rather than comparing arbitrary clock times from different schedules. This keeps the operational milestone matched while the relaxation duration varies.
The result shows thermal memory under one boundary model. It does not infer an actual formation's properties from the temperature differences.
Keep the study's claim narrow
No field measurements are used and no thermal model is ranked as more accurate. The original contribution is a reproducible schedule experiment.
A field comparison would require temperature history, boundary conditions, property uncertainty and independent observations at matched locations and times.
Explore the example
Original recorded synthetic cases solved with the site's formation-thermal-history engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Shut-in duration (h) = 24. Final wellbore temperature (K): 312.975423; Wellbore temperature at shut-in (K): 311.732495.
- Final wellbore temperature (K)
- Wellbore temperature at shut-in (K)
Worked example
Formation Thermal History, Shut-In and Restart Calculator
Fixed controls: Well/formation interface radius = 0.1 m; Distant insulated outer radius = 10 m; Formation thermal conductivity = 2.5 W/(m.K); Formation volumetric heat capacity = 2.5 MJ/(m^3.K); Wellbore thermal capacity per length = 50000 J/(m.K); Wellbore-to-formation conductance per length = 50 W/(m.K); On/restart net heat input per length = 100 W/m; Initial uniform absolute temperature = 300 K; Initial operation duration = 24 h; Restart duration = 24 h.
Relation and unit basis
Cylindrical finite volumes use exact logarithmic radial thermal resistances, rock heat capacity per annular cell and one lumped wellbore capacity per length. Piecewise constant net heat input has on/zero/restart segments. Advance each linear segment by a matrix exponential and retain cumulative heat for an independent storage balance.
Shut-in duration is varied within the supported input range. One local axial segment, uniform initial state and constant properties. No axial advection, geothermal gradient, full circulating well profile, casing-layer resolution or phase change.
1. Define the baseline
Shut-in duration (h) = 24
Fixed controls: Well/formation interface radius = 0.1 m; Distant insulated outer radius = 10 m; Formation thermal conductivity = 2.5 W/(m.K); Formation volumetric heat capacity = 2.5 MJ/(m^3.K); Wellbore thermal capacity per length = 50000 J/(m.K); Wellbore-to-formation conductance per length = 50 W/(m.K); On/restart net heat input per length = 100 W/m; Initial uniform absolute temperature = 300 K; Initial operation duration = 24 h; Restart duration = 24 h.
2. Select the relation
Cylindrical finite volumes use exact logarithmic radial thermal resistances, rock heat capacity per annular cell and one lumped wellbore capacity per length. Piecewise constant net heat input has on/zero/restart segments. Advance each linear segment by a matrix exponential and retain cumulative heat for an independent storage balance.
Shut-in duration is varied within the supported input range. One local axial segment, uniform initial state and constant properties. No axial advection, geothermal gradient, full circulating well profile, casing-layer resolution or phase change.
3. Substitute the values
off = 24 h; with the fixed controls above, the workflow evaluates Final wellbore temperature = 312.975423 K; Wellbore temperature at shut-in = 311.732495 K
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Final wellbore temperature (K) = 312.975423; Wellbore temperature at shut-in (K) = 311.732495
Prescribed net heat rate: positive heats, negative cools, and shut-in means zero external heat input, not zero wellbore-to-rock heat transfer. Steel/fluid inventory and effective conductance must be supplied consistently. Insulated distant finite domain guarded by a diffusion-length test. This is not an arbitrary-duration infinite-reservoir solution. Energy/grid checks do not establish field accuracy or replace a calibrated transient well model.
Result and interpretation
Final wellbore temperature (K) = 312.975423; Wellbore temperature at shut-in (K) = 311.732495
Prescribed net heat rate: positive heats, negative cools, and shut-in means zero external heat input, not zero wellbore-to-rock heat transfer. Steel/fluid inventory and effective conductance must be supplied consistently. Insulated distant finite domain guarded by a diffusion-length test. This is not an arbitrary-duration infinite-reservoir solution. Energy/grid checks do not establish field accuracy or replace a calibrated transient well model.
Select the recorded shut-in schedule and compare the same restart-end output.
Study data and reproduction
Original recorded synthetic cases solved with the site's formation-thermal-history engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.
| Shut-in duration (h) | Final wellbore temperature (K) | Wellbore temperature at shut-in (K) |
|---|---|---|
| 6 | 313.5121 | 311.7325 |
| 12 | 313.287 | 311.7325 |
| 24 | 312.9754 | 311.7325 |
| 48 | 312.6222 | 311.7325 |
| 72 | 312.4262 | 311.7325 |
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. Why compare a matched restart milestone instead of the same total clock time?
Show the worked answer
The schedules have different shut-in durations; equal clock time can place them in different operating phases.
2. Reproduce the baseline Final wellbore temperature (K) without rounding intermediate values.
Show the worked answer
off = 24 h; with the fixed controls above, the workflow evaluates Final wellbore temperature = 312.975423 K; Wellbore temperature at shut-in = 311.732495 K. Final wellbore temperature (K) = 312.975423. Prescribed net heat rate: positive heats, negative cools, and shut-in means zero external heat input, not zero wellbore-to-rock heat transfer. Steel/fluid inventory and effective conductance must be supplied consistently. Insulated distant finite domain guarded by a diffusion-length test. This is not an arbitrary-duration infinite-reservoir solution. Energy/grid checks do not establish field accuracy or replace a calibrated transient well model.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Shut-in duration (h) changes from 6 to 72. Other controls remain as stated in the premise. Final wellbore temperature (K) changes from 313.512055 to 312.426224.
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. Shut-in duration is varied within the supported input range. One local axial segment, uniform initial state and constant properties. No axial advection, geothermal gradient, full circulating well profile, casing-layer resolution or phase change. Prescribed net heat rate: positive heats, negative cools, and shut-in means zero external heat input, not zero wellbore-to-rock heat transfer. Steel/fluid inventory and effective conductance must be supplied consistently. Insulated distant finite domain guarded by a diffusion-length test. This is not an arbitrary-duration infinite-reservoir solution. Energy/grid checks do not establish field accuracy or replace a calibrated transient well model.
Before using the result
- Match the process milestone.
- Retain the full schedule.
- Do not interpret synthetic differences as field calibration.
Prescribed net heat rate: positive heats, negative cools, and shut-in means zero external heat input, not zero wellbore-to-rock heat transfer. Steel/fluid inventory and effective conductance must be supplied consistently. Insulated distant finite domain guarded by a diffusion-length test. This is not an arbitrary-duration infinite-reservoir solution. Energy/grid checks do not establish field accuracy or replace a calibrated transient well model.
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.