Tubing stretch: pull, own weight and temperature
Stretch of a freely hanging string from an axial pull, from its own weight in fluid and from a temperature change, and the thermal force in a string fixed at both ends (e.g. on a packer).
A = π/4 · (D² − (D − 2t)²)ΔL_F = F · L / (E · A)ΔL_w = g · L² · (ρ_s − ρ) / (2 · E)ΔL_T = α · L · ΔT; F_T = E · A · α · ΔTΔL = ΔL_F + ΔL_w + ΔL_TThe string is uniform, hangs freely and is open at the bottom; couplings and upsets are ignored (they add a few percent to the weight stretch). Fluid pressure on the wall (Poisson effect), buckling and friction are not included — for a string on a packer use a Lubinski tubing movement analysis. E = 206 800 MPa, α = 1.2·10⁻⁵ 1/°C, steel 7850 kg/m³; heating makes F_T compress a fixed string, cooling puts it in tension.
Source: Hooke's law and linear thermal expansion; Lubinski A., Althouse W. S., Logan J. L., Helical Buckling of Tubing Sealed in Packers (JPT, 1962)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Above the string's own weight; 0 for weight and temperature only.
Negative for cooling (cold fluid injected).
Unit converter for this formulaLength · Density and °API · Force and load · Temperature difference
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- ΔL_F — From the pull–
- ΔL_w — From own weight in fluid–
- ΔL_T — From the temperature change–
- F_T — Thermal force with both ends fixed–
More in Tubing and stuck pipe
Length of the free pipe above the stuck point from the stretch measured for an increase in pull — an estimate of where tubing or drill pipe is stuck.
Volume of a spotting fluid (oil, water or acid) that covers the stuck zone in the annulus with a reserve inside the pipe, the displacement volume, and the drop in bottomhole pressure caused by the lighter pill.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.