Engineering lesson
How to combine casing open hole and shoe track volumes
Calculate cased-hole annulus, open-hole annulus and shoe-track volumes as separate nonoverlapping entries. Their boundaries and diameters differ, even when the same slurry fills them.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Draw where each volume lives
The open-hole annulus uses hole diameter minus casing OD. A cased-hole annulus uses outer casing ID minus inner string OD. A shoe track is an internal casing volume over its own measured length.
A shoe track cannot be included by extending the annular interval: the fluid occupies the inside of the casing there. The distinction prevents both omitted volume and double counting.
Apply excess to the intended scope
An assumed open-hole excess might represent uncertain hole size. Applying that same percentage to a known cased annulus or shoe track is a different planning assumption and must be stated.
The worked ledger sums two annular intervals and one internal interval. It records volume before and after the explicitly selected excess so every contribution remains auditable.
Translate the combined design to sacks
Combine compatible slurry demand only after computing the separate geometric entries. Then convert barrels to cubic feet, divide by the matching yield and round for the actual batch plan.
Lead and tail slurries with different yields need separate ledgers. A single average yield can hide the fact that one design is assigned to the wrong interval.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Shoe-track length (ft) = 40. Track volume (bbl): 0.710469177; Total geometry volume (bbl): 80.6711835.
- Track volume (bbl)
- Total geometry volume (bbl)
Worked example
Two annuli and one internal shoe track
Annulus A: 8.5/5 in × 1,000 ft; B: 7.75/5 in × 1,000 ft. Shoe-track ID 4.276 in. No excess is added in this geometry-only ledger.
Relation and unit basis
Vtotal = VA + VB + π ID² Ltrack/(4 × 808.5)
Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet.
1. Define the baseline
Shoe-track length (ft) = 40
Annulus A: 8.5/5 in × 1,000 ft; B: 7.75/5 in × 1,000 ft. Shoe-track ID 4.276 in. No excess is added in this geometry-only ledger.
2. Select the relation
Vtotal = VA + VB + π ID² Ltrack/(4 × 808.5)
Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet.
3. Substitute the values
VA = 45.9; VB = 34.0607143; track = π/4 × 4.276² × 40/808.5 bbl; add the three nonoverlapping entries
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Track volume (bbl) = 0.710469177; Total geometry volume (bbl) = 80.6711835
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
Result and interpretation
Track volume (bbl) = 0.710469177; Total geometry volume (bbl) = 80.6711835
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
The selected row changes the shoe-track length while the two annular entries stay fixed.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Shoe-track length (ft) | Track volume (bbl) | Total geometry volume (bbl) |
|---|---|---|
| 0 | 0 | 79.96071 |
| 20 | 0.3552346 | 80.31595 |
| 40 | 0.7104692 | 80.67118 |
| 60 | 1.065704 | 81.02642 |
| 100 | 1.776173 | 81.73689 |
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 does a 5 in casing OD not determine shoe-track internal volume?
Show the worked answer
Internal volume requires casing ID. Wall thickness separates ID from OD, so OD alone is insufficient.
2. Reproduce the baseline Track volume (bbl) without rounding intermediate values.
Show the worked answer
VA = 45.9; VB = 34.0607143; track = π/4 × 4.276² × 40/808.5 bbl; add the three nonoverlapping entries. Track volume (bbl) = 0.710469177. The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Shoe-track length (ft) changes from 0 to 100. Other controls remain as stated in the premise. Track volume (bbl) changes from 0 to 1.77617294.
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. Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet. The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
Before using the result
- Identify annular and internal volumes separately.
- Avoid overlapping measured intervals.
- Apply each excess and yield to its stated scope.
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
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.