Engineering lesson
Why thermal history changes a shut in and restart calculation
Formation temperature carries memory of earlier heat transfer. A shut-in and restart calculation can therefore differ from a fresh calculation with the same current flow rate and initial undisturbed temperature.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Store energy in the formation
Heat conducted during production changes the radial formation-temperature field. During shut-in, that field relaxes rather than resetting instantly.
The supported history workflow represents thermal storage and conduction with explicit on, off and restart durations. Its boundary and property assumptions are part of the result.
Keep the complete schedule
A final elapsed time cannot uniquely reconstruct the sequence of heating and relaxation. Two schedules with the same total duration can have different near-well temperatures.
The explorer changes shut-in duration while preserving the heating and restart durations and all thermal properties.
Separate thermal memory from fluid chemistry
A warmer or cooler restart profile may alter conditions relevant to flow assurance, but the thermal solver does not automatically calculate hydrate or wax kinetics.
Use the appropriate equilibrium or transport model with a compatible local state if those questions are required.
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.
The selected shut-in duration changes the recorded formation-history state; the model is not reset between phases of a schedule.
Exact scenario data
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 can two wells with the same current rate have different near-well temperatures?
Show the worked answer
Their earlier heating and shut-in histories can leave different stored-energy and formation-temperature profiles.
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
- Retain the full on/off/restart schedule.
- Record radial boundary assumptions.
- Do not reset the formation state silently.
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.