Engineering lesson
Measured depth and diameter checks for a volume calculation
Volume uses measured interval length and the actual enclosing and enclosed diameters. TVD is appropriate for hydrostatic head, but it generally understates volume in a deviated interval.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Audit length and diameter before arithmetic
An annular interval extends along the well path. Its volume is area times measured length. A 1,000 ft path that gains only 600 ft of TVD still contains the full 1,000 ft of annular space.
The diameters must describe the fluid boundaries. An outer casing's nominal size is not its ID; an inner casing's ID is not its OD. Keep these labels on the interval sketch.
Make impossible inputs fail visibly
The outer boundary diameter must exceed the inner diameter. Equal values give zero idealized area, while an inverted pair is physically invalid for the stated annulus.
Check diameter units before squaring them. Mixing inches and millimetres creates a large error that multiplication by the correct length cannot repair.
Use a section ledger when geometry changes
A change in hole size, casing ID, string OD or measured interval boundary creates a new geometric entry. Do not average diameters before squaring; the average of squared diameters differs from the square of their average.
A schematic constant-area calculation also assumes no obstruction or internal equipment occupying additional space. Record any separately added or subtracted volume.
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.
Measured length (ft) = 1000. Annular volume (bbl): 45.9; Capacity (bbl/ft): 0.0459.
- Annular volume (bbl)
Worked example
Capacity multiplied by measured length
8.5 in hole around 5 in casing; the rounded library coefficient gives 0.0459 bbl/ft capacity.
Relation and unit basis
Va = 0.7854(Dh² − Do²)L/808.5
Diameters in inches, measured length in feet, volume in petroleum barrels. Capacity is Va/L.
1. Define the baseline
Measured length (ft) = 1000
8.5 in hole around 5 in casing; the rounded library coefficient gives 0.0459 bbl/ft capacity.
2. Select the relation
Va = 0.7854(Dh² − Do²)L/808.5
Diameters in inches, measured length in feet, volume in petroleum barrels. Capacity is Va/L.
3. Substitute the values
0.7854 × (8.5² − 5²) × 1,000/808.5 = 45.9 bbl
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Annular volume (bbl) = 45.9; Capacity (bbl/ft) = 0.0459
Length changes volume, while capacity is unchanged at fixed diameters.
Result and interpretation
Annular volume (bbl) = 45.9; Capacity (bbl/ft) = 0.0459
Length changes volume, while capacity is unchanged at fixed diameters.
The length sweep illustrates measured path length at one fixed cross section; it is not a depth-pressure plot.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Measured length (ft) | Annular volume (bbl) | Capacity (bbl/ft) |
|---|---|---|
| 250 | 11.475 | 0.0459 |
| 500 | 22.95 | 0.0459 |
| 1,000 | 45.9 | 0.0459 |
| 1,500 | 68.85 | 0.0459 |
| 2,000 | 91.8 | 0.0459 |
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. At capacity 0.0459 bbl/ft, how much does using 600 ft TVD instead of 1,000 ft MD omit?
Show the worked answer
18.36 bbl: (1,000 − 600) × 0.0459. That is 40% of the correct 45.9 bbl.
2. Reproduce the baseline Annular volume (bbl) without rounding intermediate values.
Show the worked answer
0.7854 × (8.5² − 5²) × 1,000/808.5 = 45.9 bbl. Annular volume (bbl) = 45.9. Length changes volume, while capacity is unchanged at fixed diameters.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Measured length (ft) changes from 250 to 2000. Other controls remain as stated in the premise. Annular volume (bbl) changes from 11.475 to 91.8.
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. Diameters in inches, measured length in feet, volume in petroleum barrels. Capacity is Va/L. Length changes volume, while capacity is unchanged at fixed diameters.
Before using the result
- Use measured interval length.
- Check each ID and OD label.
- Convert all diameters before squaring.
Length changes volume, while capacity is unchanged at fixed diameters.
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.