DrillX
Drill string volumes · field units
Drill pipe capacity and displacement, with trip volumes
Drill pipe capacity is the volume of mud inside the pipe, and drill pipe displacement is the volume of the steel itself. In field units, capacity (bbl/ft) = ID² ÷ 1029.4 and plain-end displacement (bbl/ft) = (OD² − ID²) ÷ 1029.4, with diameters in inches. For 5 in, 19.5 lb/ft pipe with a 4.276 in bore that gives 0.01776 bbl/ft of capacity and 0.00652 bbl/ft of displacement, so 10,000 ft of it holds about 178 bbl of mud and its steel displaces about 65 bbl. These two numbers drive trip-tank monitoring, slug volumes, pit volume checks and the hydrostatic loss when the hole is not kept full. This page gives the formulas, a table by pipe size, closed-end displacement, and worked trip examples.
Reference material only. Use the dimensions and adjusted weights from your pipe data sheets, and follow the rig's approved trip procedures and trip sheet. DrillX calculators are advisory.
1. The formulas
Pipe capacity
Capacity (bbl/ft) = ID² ÷ 1029.4
Open-ended displacement (plain pipe)
Displacement (bbl/ft) = (OD² − ID²) ÷ 1029.4
Closed-end displacement
Closed-end (bbl/ft) = OD² ÷ 1029.4 = capacity + displacement
Displacement from weight
Displacement (bbl/ft) ≈ weight (lb/ft) ÷ 2,747
ID and OD are in inches. The same 1029.4 constant gives annular capacity, (Dh² − OD²) ÷ 1029.4, because a barrel is 9,702 cubic inches and one foot of a 1 in bore holds 12 × π ÷ 4 = 9.4248 cubic inches; 9,702 ÷ 9.4248 = 1029.4. The weight-based form works because steel weighs about 489.5 lb/ft³, or roughly 2,747 to 2,748 lb per barrel of steel.
In metric units, capacity in litres per metre = 0.0007854 × ID² with ID in millimetres, and displacement in L/m = 0.0007854 × (OD² − ID²). Divide by 1,000 for m³/m.
2. Open-ended, closed-end and tool joints
Open-ended displacement is the steel only. It applies when the pipe is run or pulled dry: mud flows freely in and out of the bore, so the only volume entering or leaving the hole is the steel.
Closed-end displacement applies when the bore is plugged or full of mud that moves with the pipe, for example running pipe with a float valve that has not been filled, or pulling wet pipe where the mud inside comes out at surface instead of draining back into the hole. Then the hole loses steel plus the mud inside.
The plain-end formula ignores tool joints and upsets, which are thicker than the tube. On a typical joint of drill pipe they raise the steel volume per foot by roughly 10 to 20 percent, depending on the connection. For trip sheets, the usual practice is to take the adjusted (approximate) weight per foot including tool joints from the manufacturer's data sheet or IADC tables and divide by 2,747. The tube-only figures below are a lower bound.
3. Capacity and displacement by pipe size
Values for common API drill pipe sizes, calculated from nominal OD and ID with the formulas above. Displacement is tube only, without tool joints.
| Pipe OD × weight | ID (in) | Capacity bbl/ft | Displacement bbl/ft | Closed-end bbl/ft |
|---|---|---|---|---|
| 3½ in × 13.30 lb/ft | 2.764 | 0.00742 | 0.00448 | 0.01190 |
| 4 in × 14.00 lb/ft | 3.340 | 0.01084 | 0.00471 | 0.01554 |
| 4½ in × 16.60 lb/ft | 3.826 | 0.01422 | 0.00545 | 0.01967 |
| 5 in × 19.50 lb/ft | 4.276 | 0.01776 | 0.00652 | 0.02429 |
| 5½ in × 21.90 lb/ft | 4.778 | 0.02218 | 0.00721 | 0.02939 |
| 6⅝ in × 25.20 lb/ft | 5.965 | 0.03457 | 0.00807 | 0.04264 |
Drill collars have small bores and thick walls, so the balance flips. An 8 in collar with a 2-13/16 in bore holds only 0.00768 bbl/ft but displaces 0.05449 bbl/ft; a 6½ in collar with the same bore displaces 0.03336 bbl/ft. A short BHA can therefore displace as much mud as several stands of drill pipe.
4. Worked example: string volumes
10,000 ft of 5 in, 19.5 lb/ft drill pipe (4.276 in ID), tube only:
- Capacity: 4.276² ÷ 1029.4 = 0.01776 bbl/ft × 10,000 ft = 177.6 bbl of mud inside the string.
- Displacement: (5² − 4.276²) ÷ 1029.4 = 6.716 ÷ 1029.4 = 0.00652 bbl/ft × 10,000 ft = 65.2 bbl of steel.
- Closed-end: 5² ÷ 1029.4 = 0.02429 bbl/ft × 10,000 ft = 242.9 bbl.
String capacity is what you need for surface-to-bit strokes: divide 177.6 bbl by the pump output per stroke. Add annular volume for a full circulation, and use both when building a kill sheet.
5. Worked example: trip tank volumes
Pulling out of hole with the same 5 in pipe, five stands at a time (5 × 93 ft = 465 ft), inside 9⅝ in, 47 lb/ft casing with an 8.681 in ID (casing capacity 8.681² ÷ 1029.4 = 0.07321 bbl/ft) and 10 ppg mud:
| Case | Volume to fill per 5 stands | Level drop if not filled | Hydrostatic lost |
|---|---|---|---|
| Pulling dry (open-ended) | 465 × 0.00652 = 3.03 bbl | 3.03 ÷ (0.07321 − 0.00652) = 45 ft | 0.052 × 10 × 45 = 24 psi |
| Pulling wet (closed-end) | 465 × 0.02429 = 11.29 bbl | 11.29 ÷ (0.07321 − 0.02429) = 231 ft | 0.052 × 10 × 231 = 120 psi |
The hydrostatic loss is why the hole must be kept full. Turned around, the same relationship gives the length that can be pulled before a given overbalance is gone: feet = overbalance × (casing capacity − displacement) ÷ (0.052 × MW × displacement). With 100 psi of overbalance in this example, that is about 1,966 ft dry but only about 387 ft wet.
On a trip sheet the measured fill is compared with the calculated volume after each stand or group of stands. A hole taking less than calculated may be swabbing or flowing (see swab and surge pressure); a hole taking more is losing mud. Either is a reason to stop and check, following the rig's procedures.
6. Common mistakes
- Using tube-only displacement on the trip sheet. Leaving out tool joints understates the fill volume, so a hole that is taking the right volume can look like it is losing mud.
- Mixing dry and wet. After a slug is pumped the pipe is pulled dry; without one, or if the slug did not work, it may come out wet. Use the case that matches what you see at the rotary table.
- Forgetting the BHA. Collars, heavy-weight pipe and jars displace far more per foot than drill pipe and should be on their own lines of the trip sheet.
- Nominal instead of actual ID. Internal coatings, wear and different weight grades change the bore. Use the ID for the pipe actually in the string.
- Unit slips. 1029.4 is for inches and barrels per foot. With millimetres and litres per metre the factor is 0.0007854.
The same 1029.4 capacity arithmetic, applied to casing and the open-hole annulus, gives slurry and displacement volumes for a casing job: see cement volume calculation.
7. In DrillX
DrillX includes calculators for hydrostatic pressure, ECD, annular pressure loss, annular capacity and velocity, buoyancy and string weight (used for free point estimates on stuck pipe), pump output and a kill sheet, alongside daily drilling reports that flag lost time (see IADC DDR codes explained). Calculators are advisory and do not replace the rig's trip sheet or procedures. DrillX opens soon; email info@drillx.app for a demo or early access.
Questions
What is the formula for drill pipe capacity?
Drill pipe capacity in barrels per foot equals the inside diameter in inches squared divided by 1029.4. For 5 in, 19.5 lb/ft drill pipe with a 4.276 in ID, capacity is 4.276² ÷ 1029.4 = 0.01776 bbl/ft, or about 177.6 bbl per 10,000 ft.
What is the formula for drill pipe displacement?
Plain-end (open-ended) displacement in barrels per foot equals the outside diameter squared minus the inside diameter squared, divided by 1029.4. For 5 in pipe with a 4.276 in ID it is (25 − 18.284) ÷ 1029.4 = 0.00652 bbl/ft. Tool joints add to this, so for trip calculations use the adjusted weight per foot from the pipe data sheet divided by about 2,747 lb/bbl.
What is closed-end displacement?
Closed-end displacement is the volume a pipe pushes aside when it is full of mud or plugged, so the mud inside moves with it. It equals capacity plus open-ended displacement, or OD² ÷ 1029.4 for plain-end pipe: 0.02429 bbl/ft for 5 in drill pipe.
Where does 1029.4 come from?
One US oilfield barrel is 42 gallons or 9,702 cubic inches. A one-foot length of pipe with a 1 in bore holds 12 × π ÷ 4 = 9.4248 cubic inches, so a pipe with bore d holds 9.4248 × d² cubic inches per foot, and 9,702 ÷ 9.4248 = 1029.4.
How much mud should it take to fill the hole when pulling pipe?
When pulling dry pipe, the hole should take the steel displacement of the pipe pulled; when pulling wet pipe with the mud draining to the flowline or a mud bucket, it should take the closed-end displacement. Five stands (about 465 ft) of 5 in pipe need about 3.0 bbl dry or 11.3 bbl wet. If the trip tank shows less, the well may be flowing.
How far does the mud level drop if the hole is not filled?
Level drop in feet equals the volume of steel or pipe removed divided by the casing capacity minus the pipe's displacement. Pulling 465 ft of 5 in pipe dry in 9⅝ in, 47 lb/ft casing without filling drops the level about 45 ft, which removes about 24 psi of hydrostatic pressure with 10 ppg mud.
Sources and further reading
- Norton J. Lapeyrouse, Formulas and Calculations for Drilling, Production and Workover (Gulf Professional Publishing): capacity, displacement and the feet-of-pipe-pulled-to-lose-overbalance formulas for dry and wet pipe.
- A. T. Bourgoyne Jr. et al., Applied Drilling Engineering, SPE Textbook Series Vol. 2 (Society of Petroleum Engineers, 1986).
- API Specification 5DP, Drill Pipe (American Petroleum Institute): drill pipe sizes, weights and dimensions.
- IADC Drilling Manual (International Association of Drilling Contractors): drill string data and trip practices.
- SLB Energy Glossary, trip tank and related terms: glossary.slb.com