Drilling line · field units

Ton-mile calculation for drilling line: formulas and slip-and-cut

A ton-mile is the work done by the drilling line in moving one ton (2,000 lb) a distance of one mile (5,280 ft), which is 10,560,000 ft·lb. The round-trip formula in field units is Tr = [D × (Ls + D) × Wm + 4 × D × (M + ½C)] ÷ 10,560,000, where D is depth, Ls is stand length, Wm is buoyed drill pipe weight per foot, M is the weight of the travelling equipment and C is the excess buoyed weight of the BHA. Drilling, coring, short trips and casing runs are all worked out from round-trip values. The running total tells the crew when to slip and cut the drilling line under the rig's cut-off program. This page sets out each formula with a worked example.

Reference material only. Ton-mile limits between slips and cuts, cut length and line replacement must come from the rig's drilling line program, the wire rope manufacturer and your contractor's procedures, normally based on API RP 9B. DrillX calculators are advisory.

1. Why ton-miles matter

The drilling line wears where it bends over the crown and travelling block sheaves and where it wraps on the drawworks drum. Work done by the line, measured in ton-miles, is the accepted way to track that wear. When the running total reaches the figure set in the rig's program, the crew slips new line from the supply reel through the system, moving the worn sections off the critical points, and cuts the used length off the drum. Recording ton-miles for every trip, drilling interval, coring run and casing job is what makes the slip-and-cut schedule work.

2. The formulas

• D: depth of the trip, ft.
• Ls: average length of one stand, ft (about 93 ft for triples of Range 2 pipe).
• Wm: weight of drill pipe in mud, lb/ft. Use the adjusted weight including tool joints, multiplied by the buoyancy factor.
• M: total weight of the travelling block, hook, top drive or kelly and elevators, lb.
• C: buoyed weight of the BHA minus the buoyed weight of the same length of drill pipe, lb.
• T1, T2: round-trip ton-miles at the depth where drilling started and where it stopped. T3, T4: the same for coring. T5: round trip at the depth the short trip was pulled to; T6: round trip at the depth it started from.

10,560,000 is 2,000 lb per ton × 5,280 ft per mile. The first term covers the drill pipe, which is lifted out a stand at a time. The second covers the travelling equipment and the heavy BHA, which travel the full depth both ways.

Drilling multiplier. The factor 3 assumes each joint is drilled down, picked up and reamed once before the connection. Some programs use 2 for drilling without reaming and 4 for reaming twice; use the factor in your own program.

Casing. Casing work is calculated with the round-trip formula using the casing joint length and buoyed casing weight, with C = 0, and taken as one half of that result because the casing only goes in the hole. Follow the exact casing formula in your contractor's procedure.

3. Worked example

Excess BHA weight: C = 600 × (147 − 21.9) × 0.8473 ≈ 63,600 lb.

Drilling the 1,000 ft interval puts about 233 ton-miles on the line, and the trip out at 11,000 ft adds another 659. The pipe term is the larger share at depth because it grows with D², which is why ton-miles climb quickly in deep wells.

4. Slip and cut

The rig's drilling line program, normally built on API RP 9B, sets the ton-miles allowed between cuts and the length to cut. The length depends on the drum diameter, the number of drum wraps and the derrick height, and is chosen so that worn sections move off the crown sheaves and the drum crossover points rather than simply cycling back onto them. A typical routine is:

• Log ton-miles for every trip, drilling interval, coring run, wiper trip and casing job.
• Keep a running total since the last cut and compare it with the program's limit.
• When the limit is reached, plan the slip and cut, usually at a casing point or with the BHA in the shoe.
• Slip the line through, cut the length set in the program, reset the counter and record line remaining on the supply reel.
• Inspect the line, re-check the crown saver and block height settings, and record the job.

Many rigs also slip line between cuts to spread wear, and cut early after a jarring job, heavy fishing work or a hard stop.

5. Mistakes to avoid

• Using nominal pipe weight instead of adjusted weight including tool joints.
• Using the air weight of the pipe and BHA instead of buoyed weight.
• Leaving the top drive out of M.
• Adding drilling ton-miles but forgetting wiper trips, reaming and casing runs.
• Mixing feet and metres. The constants here are for feet and pounds.
• Treating ton-miles as the only measure of line condition. Broken wires, kinks, crushing and corrosion call for a cut or replacement whatever the counter says.

How DrillX helps

DrillX is drilling operations software in final testing. Its calculators cover hydrostatic pressure, ECD, annular pressure loss, MAASP from leak-off test, triplex pump output, annular capacity and velocity, buoyancy and string weight and a Driller's and Wait & Weight kill sheet, in English or Arabic. Email info@drillx.app for a demo or early access, or see what DrillX does.

Sources and further reading

• API Recommended Practice 9B, Application, Care, and Use of Wire Rope for Oil Field Service: api.org
• SLB Energy Glossary, slip and cut: glossary.slb.com
• ogPypeline drilling formulas (round trip, drilling, coring, casing and short-trip ton-miles): ogpypeline.readthedocs.io