String weight · field units

Buoyancy factor formula and buoyed string weight

The buoyancy factor for steel pipe in drilling mud, in field units, is BF = (65.5 − MW) ÷ 65.5, which is the same as 1 − MW ÷ 65.5, where MW is mud weight in ppg and 65.5 ppg is the density of steel. Multiply the weight of the string in air by BF to get its weight in mud. In 12.0 ppg mud, BF = 1 − 12.0 ÷ 65.5 = 0.8168, so 220,000 lb of drill pipe in air weighs about 179,700 lb in the hole. This page sets out the formulas, a worked example for drill pipe and collars, the general formula for different fluids inside and outside the pipe, and how buoyed weight feeds into hook load and weight on bit.

Reference material only. Hook load, overpull and weight-on-bit limits must come from your well program, the pipe and rig ratings and your company's approved procedures. DrillX calculators are advisory.

1. What buoyancy does to a drill string

A string hanging in mud is pushed up by the fluid it displaces, as Archimedes' principle describes, so it weighs less in the hole than on the pipe rack. The weight indicator reads this reduced, buoyed weight. Heavier mud displaces more weight, so the string becomes lighter as mud weight rises. The buoyancy factor is simply the fraction of the air weight that remains.

Buoyed weight is used every day on a rig: to predict hook load and overpull, to pick a weight on bit the BHA can actually deliver, to check the hoisting system and derrick against the heaviest string, and to compare the weight indicator with what the string should weigh.

2. The formulas

MW is mud weight in ppg and SG is mud specific gravity. 65.5 ppg and SG 7.85 are the density of steel in each unit system. In the collar formula OD and ID are in inches; the constant 2.67 combines π ÷ 4, 12 inches per foot and the density of steel (about 0.2833 lb per cubic inch). It gives the weight of a plain collar and does not allow for spiral grooves or recesses.

Where 65.5 comes from. Steel weighs about 489.5 lb per cubic foot. One cubic foot holds 7.48 US gallons, so steel's density is 489.5 ÷ 7.48 ≈ 65.5 lb per gallon. A string in mud weighing MW ppg loses MW ÷ 65.5 of its weight, which leaves 1 − MW ÷ 65.5.

3. Worked example

With the string off bottom in a vertical hole, the weight indicator should read about 251,700 lb plus the weight of the travelling block, top drive and other hoisting equipment, if the indicator has not been zeroed with them hanging. Friction, hole angle and pipe that is still moving all change the reading, which is why a measured pick-up and slack-off weight is taken on the rig and compared with the calculated figure.

4. Buoyancy factor by mud weight

MW is mud weight, SG is specific gravity and BF is the buoyancy factor. Fresh water at 8.33 ppg already takes almost 13% off the string's weight. Each extra ppg of mud removes roughly another 1.5% of the air weight.

5. Different fluids inside and outside the pipe

The simple formula assumes the same mud inside the string and in the annulus. That is not true while pumping a heavy slug before a trip, displacing to a new mud weight, cementing, or running casing that is not yet full. Then the general form applies:

Ao and Ai are the areas enclosed by the pipe's outside and inside diameters (π ÷ 4 × OD² and π ÷ 4 × ID²), MWo is the annulus mud weight and MWi is the mud weight inside the pipe. Heavier fluid inside the string makes it heavier at the hook; an empty or partly filled casing string floats and can weigh far less than expected, which matters when running casing with a float valve.

6. Buoyed weight, weight on bit and the neutral point

Drill pipe is not designed to run in compression in a vertical well. Weight on bit should therefore come from the drill collars and heavy-weight drill pipe, so that the neutral point, the point in the string between tension above and compression below, stays inside the BHA. The weight the BHA can give is its buoyed weight, not its air weight. In the example above the 600 ft of collars weigh 88,200 lb in air but only about 72,000 lb in 12.0 ppg mud. Many operators set maximum weight on bit as a fraction of buoyed BHA weight, commonly around 80% to 85%, to keep a margin; follow the figure in your own well program.

In a deviated hole only the component of weight along the hole axis pushes the bit, roughly the buoyed weight multiplied by the cosine of the inclination before friction is considered, so a BHA that is ample in a vertical well can be short of weight at high angle.

7. Where buoyed weight is used

• Hook load and overpull. Expected string weight plus the allowed overpull must stay within the rating of the pipe, the hoisting system and the derrick. The same buoyed hookload is the starting point for a free point estimate on stuck pipe.
• Weight on bit. BHA design and the neutral point, as above.
• Trip monitoring. Pick-up and slack-off weights that drift from the calculated buoyed weight are an early sign of drag or hole problems.
• Mud weight changes. Raising mud weight to control a well, using the kill sheet, also lightens the string. See hydrostatic pressure for how mud weight converts to pressure.
• Casing runs. Long, heavy casing strings are checked against rig capacity using buoyed weight, with the internal fluid accounted for.
• Drilling line wear. Buoyed pipe and BHA weights are the inputs to the ton-mile calculation that sets when the drilling line is slipped and cut.

8. Mistakes to avoid

• Using nominal drill pipe weight instead of adjusted weight that includes the tool joints.
• Using the air weight of the BHA when choosing weight on bit.
• Applying the simple formula when a heavy slug or a different mud is inside the pipe.
• Mixing units: 65.5 goes with ppg, 7.85 goes with specific gravity.
• Forgetting the block and top drive when comparing a calculated weight with the weight indicator.
• Treating the calculated weight as exact in a deviated or tight hole, where friction can add or remove tens of thousands of pounds.

How DrillX helps

DrillX includes a buoyancy and string weight calculator alongside hydrostatic pressure, ECD, annular pressure loss, MAASP from leak-off test, annular capacity and velocity, triplex pump output, and a Driller's and Wait & Weight kill sheet. Values update as you type, in field units, and in English or Arabic. DrillX is in final testing; email info@drillx.app for a demo or early access, or see what DrillX does. For the mud inside the string and the volume its steel displaces on trips, see drill pipe capacity and displacement.

Sources and further reading

• SLB Energy Glossary, neutral point: glossary.slb.com
• SLB Energy Glossary, hook load: glossary.slb.com
• International Association of Drilling Contractors, WellSharp well-control training: iadc.org/wellsharp