Drilling guides › Hole volume, pipe capacity and annular capacity
Hole volume, pipe capacity and annular capacity
Volumes decide how many strokes it takes to pump mud to the bit, how long bottoms-up takes and how much mud a trip needs. They all come from one simple formula. They also feed the kill sheet, the cement job and the pit volume you need on surface, so a small error here travels a long way.
Capacity of a hole or a pipe
Use the inside diameter of the pipe, or the bit size (or caliper size) for open hole. The constant 1029.4 comes from one barrel being 9,702 cubic inches: 9,702 ÷ (π/4 × 12 inches per foot) = 1029.4.
In other words, a one-foot slice of a cylinder holds π/4 × ID² × 12 cubic inches, and dividing by the cubic inches in a barrel turns that into barrels. The metric constant works the same way: 1273.2 is 4 ÷ π × 1,000, because a litre is a million cubic millimetres and a metre is a thousand millimetres.
Annular capacity
Inside casing, use the casing ID instead of the bit size. Work each section separately (riser, casing, open hole; drill pipe, heavy-weight, collars) and add them up.
The annulus is simply the big circle minus the small one, so the squares are subtracted before dividing. Never subtract the diameters first: (8.5 − 5)² gives 12.25, not 47.25, and the volume would be wrong by a factor of almost four.
Worked example: 5 in drill pipe in 8½ in hole
| Item | Sum | Result |
|---|---|---|
| Open hole 8.5 in | 8.5² ÷ 1029.4 | 0.0702 bbl/ft |
| 5 in DP, ID 4.276 in | 4.276² ÷ 1029.4 | 0.0178 bbl/ft |
| Annulus 8.5 in × 5 in | (72.25 − 25) ÷ 1029.4 | 0.0459 bbl/ft |
With 10,000 ft of drill pipe (ignoring the BHA and casing to keep it short):
In metric, the 8½ in (215.9 mm) hole holds 215.9² ÷ 1273.2 = 36.6 litres per metre.
Worked example: a well with casing and a BHA
Bit at 10,000 ft. 9⅝ in 47 lb/ft casing (ID 8.681 in) to 6,000 ft, then 8½ in open hole. String: 9,400 ft of 5 in drill pipe (ID 4.276 in) and 600 ft of 6½ in collars (ID 2.8125 in).
| Section | Capacity (bbl/ft) | Length (ft) | Volume (bbl) |
|---|---|---|---|
| Casing × DP annulus | (8.681² − 5²) ÷ 1029.4 = 0.0489 | 6,000 | 293.5 |
| Open hole × DP annulus | 0.0459 | 3,400 | 156.1 |
| Open hole × collars | (72.25 − 42.25) ÷ 1029.4 = 0.0291 | 600 | 17.5 |
| Drill pipe bore | 0.0178 | 9,400 | 167.0 |
| Collar bore | 2.8125² ÷ 1029.4 = 0.0077 | 600 | 4.6 |
Notice how little the collars add to the string volume, and how much the casing section dominates the annulus. Shortcuts that treat the whole annulus as open hole would have underestimated it by about 18 bbl here, and more in a well with a longer casing string.
Steel displacement
Displacement is the volume of the steel itself: how much mud the pipe pushes out when it goes in the hole open-ended.
For 5 in pipe with a 4.276 in ID this gives 0.0065 bbl/ft for the tube alone. Tool joints add to it, so for trip sheets use the adjusted displacement from the pipe data sheet (often about 0.0075 bbl/ft for 5 in 19.5 lb/ft pipe).
Closed-end displacement
When the pipe is run with a float or pulled wet, the mud inside moves with it. The closed-end displacement is the steel displacement plus the pipe capacity, which is simply OD² ÷ 1029.4 (0.0243 bbl/ft for 5 in pipe, before tool joints).
Where these numbers are used
- Kill sheets: string volume gives strokes to bit; annulus volume gives strokes from bit to surface.
- Bottoms-up and lag time: the mud logger uses the annulus volume to tie each sample to the depth it came from.
- Cementing: annular volume between casing and hole, plus excess, sets the slurry volume; casing capacity sets the displacement.
- Trips: displacement and capacity give the expected hole fill.
A useful cross-check
The volume of the hole with no pipe in it should equal the circulating volume plus the steel displacement of the string. In the casing-and-BHA example above, the empty hole holds 0.0732 × 6,000 + 0.0702 × 4,000 = 720 bbl. The tube displacement of the drill pipe (0.0065 × 9,400 ≈ 61 bbl) and the collars (0.0334 × 600 ≈ 20 bbl) adds 81 bbl to the 638.7 bbl circulating volume, giving the same 720 bbl. When the two sides do not match, one of the diameters or lengths in the table is wrong.
This empty-hole volume is also the mud the well needs when the string is out of the hole, which matters when planning a displacement to a new mud system or a weight-up with the pipe out.
Metric example
A 311 mm (12¼ in) hole with 127 mm (5 in) drill pipe has an annular capacity of (311.15² − 127²) ÷ 1273.2 ≈ 63.4 L/m. The oilfield figure, 0.1215 bbl/ft, multiplied by 521.6 (litres per metre in one bbl/ft) gives the same 63.4 L/m.
Common mistakes
- Using the nominal size of casing or drill pipe instead of the real ID. Casing of the same OD has a different ID for each weight.
- Taking the tool joint OD for the annulus over the whole length, or the tube OD for displacement on a trip sheet.
- Forgetting the surface lines, the riser or a liner lap.
- Using bit size for an open hole that is badly washed out.
Good practice
- Keep a section-by-section volume table and update it after every casing point and BHA change.
- Check calculated bottoms-up against a real one: time a marker such as a carbide or a change in mud weight and compare it with the calculation.
- Use the pipe tally for lengths, not round numbers.