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Drilling problems · field units
Stuck pipe: differential vs mechanical, and the free point formula
Stuck pipe means the drill string cannot be moved out of the hole without exceeding the safe overpull or torque of the string. It falls into two groups. Differential sticking happens when the overbalance holds a stationary string against the mudcake of a permeable zone; circulation stays free. Mechanical sticking happens when cuttings, unstable formation, hole geometry or junk physically block the string, usually while it is moving. Once the pipe is stuck, the free point, the depth above which the string is still free, is estimated from stretch with Hooke's law: free pipe (ft) = stretch (in) × pipe-body area (sq in) × 2,500,000 ÷ differential pull (lb). This page explains how to tell the mechanisms apart, gives the sticking-force and free point formulas with worked examples, and lists the usual first actions.
Reference material only. Stuck pipe response, jarring limits and overpull must follow your company's approved procedures, the string design and the rig's equipment ratings. Worked examples are illustrative arithmetic.
1. The mechanisms
Differential sticking
Mud pressure is higher than formation pressure, so the string is pressed into the mudcake of a permeable sand or carbonate. It is most likely when the string is left stationary, for example during a connection or a survey, with drill collars against a depleted or overbalanced zone.
Pack-off and bridging
Cuttings that are not cleaned out of the hole settle when circulation stops, or build a bed on the low side of a deviated hole, and pack around the BHA (see hole cleaning and cuttings transport). Unstable shale that sloughs or swells, and unconsolidated formations that collapse, act the same way.
Wellbore geometry
Keyseats worn by the string in a dogleg, ledges at hard-soft interbeds, undergauge hole after a worn bit, and a stiff new BHA run into a hole drilled with a limber one. The pipe sticks while moving, and circulation is normal.
Junk and cement
Hand tools, broken bit or BHA parts and lumps of cement falling from the casing shoe or a plug jam the string. Green cement can also set around a string run in too early.
Hole problems that cause stuck pipe overlap with other NPT causes: tight hole, lost circulation and well control events often come together. In daily reports the time is logged as stuck pipe or fishing; see IADC DDR codes and NPT in drilling for how it is counted.
2. How to tell which one it is
The three questions that sort most cases are: what was the pipe doing just before it stuck, can it still move or rotate, and can you circulate.
| Check | Differential | Pack-off / bridge | Wellbore geometry |
|---|---|---|---|
| Pipe motion before sticking | Static | Moving, often pulling out | Moving up or down |
| Movement after sticking | None, up or down | Restricted up and down, or none | Often free in the opposite direction |
| Rotation after sticking | Not possible | Restricted or none | Usually possible |
| Circulation | Free, normal pressure | Restricted or lost, pressure rising | Free, normal pressure |
| Typical warning signs | Rising torque and drag across a permeable zone, overpull after connections | Rising pump pressure, erratic torque, cuttings returns drop, overpull on trips | Sudden overpull at the same depth on each trip, after several stands are pulled |
PetroWiki lists the same signs for differential sticking: rising torque and drag, inability to reciprocate and sometimes rotate the string, while circulation continues uninterrupted. Mechanical sticking is flagged by rising circulating pressure, increased torque and drag and, for keyseats, sticking after several stands have been pulled.
3. Differential sticking force
Overbalance
ΔP (psi) = 0.052 × (MW − pore EMW) × TVD
Sticking force
F (lb) = f × ΔP × Ac
Contact area
Ac (sq in) = contact width (in) × embedded length (ft) × 12
Friction coefficient f
< 0.04 oil-based mud … 0.35 weighted water-based mud
The friction range is the one PetroWiki gives for mud without lubricants. Contact width grows as the mudcake thickens and as the pipe sinks into it, which is why sticking force rises the longer the string stays stuck. Worked example: 11.0 ppg mud across a sand at 9,000 ft TVD with a pore pressure equal to 8.9 ppg.
| Step | Working | Answer |
|---|---|---|
| Overbalance | 0.052 × (11.0 − 8.9) × 9,000 | 983 psi |
| Contact area | 2 in wide × 30 ft of collars × 12 | 720 sq in |
| Sticking force, f = 0.20 | 0.20 × 983 × 720 | ≈ 142,000 lb |
| Same, f = 0.04 | 0.04 × 983 × 720 | ≈ 28,000 lb |
Even a modest contact patch can hold more than the available overpull, which is why prevention matters more than freeing: keep the overbalance no higher than the well needs, keep fluid loss and drilled solids low so the mudcake stays thin and slick, and keep the string moving across permeable zones. Overbalance comes straight from hydrostatic pressure, and while circulating the effective figure is set by ECD.
4. The free point formula
Steel stretches in proportion to load (Hooke's law): stretch = F × L ÷ (A × E). Only the free part of the string stretches, so measuring the stretch for a known extra pull gives the free length. With E = 30,000,000 psi for steel, stretch in inches and length in feet:
Free pipe from body area
L (ft) = e (in) × As (sq in) × 2,500,000 ÷ ΔF (lb)
Pipe-body area
As (sq in) = 0.7854 × (OD² − ID²)
Free point constant
FPC = As × 2,500 → L (ft) = e × FPC ÷ ΔF (1,000 lb)
From weight per foot
L (ft) = 735,294 × e × Wpe ÷ ΔF (lb)
The 2,500,000 is 30,000,000 ÷ 12. The weight form uses the fact that steel weighs about 3.4 lb per foot for every square inch of section (490 lb/cu ft ÷ 144), so As ≈ W ÷ 3.4 and 2,500,000 ÷ 3.4 = 735,294. Use the plain-end weight of the pipe body, not the nominal or adjusted weight that includes tool joints, or the free point comes out too deep. The buoyed string weight is the starting hookload for the test.
5. Worked example: free point from stretch
A string of 5 in 19.50 lb/ft drill pipe (ID 4.276 in, plain-end weight about 17.93 lb/ft) is differentially stuck. The procedure is to pull a first load a little above the free hookload to take out slack and mark the pipe at the rotary table, then pull a second, higher load and measure how far the mark has moved. Using two pulls, rather than measuring from the free hookload, cancels most of the slack and the bend in the string.
| Step | Working | Answer |
|---|---|---|
| Pipe-body area | 0.7854 × (5.000² − 4.276²) = 0.7854 × 6.716 | 5.275 sq in |
| Free point constant | 5.275 × 2,500 | ≈ 13,190 |
| Differential pull | Second pull − first pull | 40,000 lb |
| Measured stretch | Movement of the mark | 24 in |
| Free pipe | 24 × 5.275 × 2,500,000 ÷ 40,000 | ≈ 7,910 ft |
| Check, plain-end weight | 735,294 × 24 × 17.93 ÷ 40,000 | ≈ 7,910 ft |
| Wrong: nominal weight | 735,294 × 24 × 19.5 ÷ 40,000 | ≈ 8,600 ft (about 9% too deep) |
If the string is a combination of sizes, for example heavyweight pipe below drill pipe, calculate the stretch of each section separately: work down from surface, subtract the stretch the upper section accounts for over its full length, and convert the remainder with the next section's area. In deviated holes wall friction absorbs part of the pull, so the free point is shallower in reality than the stretch suggests. The figure is a plan; a wireline free-point indicator is normally run to find the actual free point before a back-off with a string shot, as described in pipe recovery practice.
6. Overpull limit
Before working the pipe, the driller needs the maximum pull that can be applied at surface without yielding the weakest part of the string: maximum overpull = (tensile rating × design factor) − free hookload. Take the tensile rating for the pipe's grade and wear class from API RP 7G or the pipe supplier, and the design factor from the well programme; 90% of the rating is a common choice. With an illustrative premium-class tensile rating of 500,000 lb, a 0.9 factor and a free hookload of 260,000 lb, the margin is 0.9 × 500,000 − 260,000 = 190,000 lb. Jars, top drive, derrick and drill line ratings may be lower than the pipe and then they set the limit.
7. First actions by mechanism
- Differential: act immediately, because sticking force grows with time. Work torque down the string and slack off to set weight down, jar down if jars are in the string, and keep circulating at normal rate. If that fails, spot a pipe-freeing fluid or oil across the stuck zone, or reduce the hydrostatic pressure where well control allows (PetroWiki lists diluting or gasifying the mud and setting a packer above the stuck point). Washing over is the fishing option.
- Pack-off: reduce pump pressure at once to avoid packing the annulus tighter, then try to re-establish circulation slowly. Work the pipe in the direction opposite to the last movement, usually down when stuck pulling out, with torque. Once circulation is back, clean the hole before moving on, within the allowable ECD.
- Wellbore geometry: jar in the direction opposite to the movement when the pipe stuck. Keyseats are passed by back-reaming or with a keyseat wiper, and ledges by reaming.
- Plan the decision point. When to stop jarring and move to free point, back-off and fishing, or plug back and sidetrack, is an economic decision normally made by the operator; agreeing the time limit before the job saves rig time.
8. In DrillX
DrillX daily drilling reports use IADC-style time logs and flag lost time, so stuck pipe and fishing hours show up in the NPT view by cause. The engineering calculators include hydrostatic pressure, ECD, buoyancy and string weight and annular capacity and velocity. A free point calculator is not listed in DrillX; the method is worked by hand above. DrillX is in final testing; email info@drillx.app for a demo or early access, or see what DrillX does.
Questions
What is stuck pipe in drilling?
Pipe is stuck when the drill string cannot be pulled out of the hole, or moved at all, without exceeding the safe overpull or torque limits of the string and rig. The two broad groups are differential sticking, where the pipe is held against a permeable formation by the overbalance, and mechanical sticking, where cuttings, unstable formation, hole geometry or junk physically block the string.
How do you tell differential sticking from mechanical sticking?
Differential sticking usually happens when the string has been stationary opposite a permeable zone: the pipe cannot be moved up or down or rotated, but circulation is free at normal pressure. Pack-off and bridging usually happen while the pipe is moving, with circulation restricted or lost. Wellbore geometry sticking, such as a keyseat or ledge, happens while moving, circulation stays free and the pipe can often still move in the opposite direction.
What is the formula for differential sticking force?
Sticking force equals the friction coefficient times the differential pressure times the contact area: F = f × ΔP × Ac. With 983 psi overbalance, 720 square inches of contact and a friction coefficient of 0.2, the force is about 142,000 lb. PetroWiki gives friction coefficients from below 0.04 for oil-based mud to as much as 0.35 for weighted water-based mud without lubricants.
What is the free point formula?
From Hooke's law, the length of free pipe in feet equals the measured stretch in inches times the pipe-body cross-sectional area in square inches times 2,500,000, divided by the differential pull in pounds. The constant 2,500,000 is the modulus of elasticity of steel, 30,000,000 psi, divided by 12 to turn inches of stretch into feet of pipe.
What is the free point constant?
The free point constant (FPC) is the pipe-body area in square inches multiplied by 2,500, so that free pipe in feet equals stretch in inches times FPC divided by the differential pull in thousands of pounds. For 5 in 19.50 lb/ft drill pipe with a 4.276 in ID the body area is 5.275 sq in and the FPC is about 13,190.
How accurate is a free point calculated from stretch?
It is an estimate. Wall drag in deviated wells, pipe wear, tool joints, mixed strings and tension lost to friction all affect the result, so the calculated depth is used to plan the job and a wireline free-point indicator tool is normally run to confirm the actual free point before a back-off.
Sources and further reading
- PetroWiki, Differential-pressure pipe sticking: sticking force from differential pressure, friction coefficient and contact area; friction coefficients from below 0.04 (oil-based mud) to 0.35 (weighted water-based mud); warning signs and freeing methods.
- PetroWiki, Mechanical pipe sticking: hole cleaning, keyseats, shale and salt instability, warning signs and freeing guidance.
- PetroWiki, Stuck pipe and SPE Petroleum Engineering Handbook, Drilling Problems and Solutions.
- Wikipedia, Pipe recovery operations: free-point tools, string-shot back-off and fishing.
- A. T. Bourgoyne Jr. et al., Applied Drilling Engineering, SPE Textbook Series Vol. 2 (1986): pipe sticking and drill string design.
- N. J. Lapeyrouse, Formulas and Calculations for Drilling, Production and Workover, 2nd ed. (Gulf Professional Publishing, 2002): free point and stretch calculations.
- API RP 7G, Recommended Practice for Drill Stem Design and Operating Limits: tensile ratings by grade and class.
Reference summary only. Worked examples are illustrative arithmetic. Overpull, jarring and freeing procedures are set by your operator's drilling programme and the equipment ratings.