Pipe Stretch

Pipe stretch is the increase in length of a drillstring, casing string, or tubing string that results from the forces acting on it inside the wellbore. The main contributors to stretch are tensile load (the weight of pipe hanging below any reference point), internal pressure (which expands the pipe lengthwise when it pushes on the closed end of the string), temperature change (thermal expansion when hot downhole fluids heat the steel), and the ballooning effect of pressure difference between the inside and outside of the pipe. Engineers calculating where a packer is set, where a perforating gun will fire, or how deep a completion tool is landed must account for all of these stretch components to predict the true position of downhole equipment within a few metres or less.

Key Takeaways

The elastic stretch due to pipe weight (often called the Hooke's Law stretch) is proportional to the total length of pipe, the weight per unit length, and inversely proportional to the cross-sectional area and Young's modulus of the steel. In a 4,000-metre tubing string with 2.375-inch tubing, this stretch can exceed 3 metres.
Pressure-induced stretch has two components: the piston effect (pressure acts on the area difference at any restriction in the string, such as a packer or plug, pushing the pipe away from the restriction) and the ballooning effect (internal pressure greater than external pressure causes the pipe to lengthen because the pressure differential makes the pipe swell radially, shortening axially, or to elongate when internal is less than external).
Temperature stretch is significant in steam injection wells (SAGD and cyclic steam stimulation) and geothermal wells, where tubing temperature can rise 100 to 200°C above the ambient setting temperature. Steel expands at approximately 12 parts per million per degree Celsius. A 200°C temperature rise over 500 metres of tubing adds about 1.2 metres of stretch.
In perforating, uncorrected stretch errors place the perforating gun at the wrong depth relative to the perforations in the casing, which can result in gun firing in casing collar or cement rather than in the sand. Modern wireline depth control uses casing collar locator (CCL) signals to correlate true position against the original openhole log depth.
Packer set depth is critical in SAGD producer wells, where the packer must seal a specific annular interval and cannot be set above or below the target window. Thermal expansion stretch calculations are part of the packer setting procedure in SAGD completion engineering.

Why Pipe Stretch Matters

Steel is stiff, but it is not infinitely stiff. Hang a long enough steel cable and the weight at the bottom will stretch the cable measurably. Do the same with a drill pipe string and the same physics applies. A 4,000-metre string of 5-inch drill pipe weighs approximately 700,000 newtons in air. The bottom 100 metres of that string hangs from the pipe above it; the top 100 metres supports all the pipe below it. The stress is highest at the top and decreases to zero at the bottom (or at the neutral point, where the string transitions from tension to compression under the weight of the drill collars and bit weight).

Because steel has a Young's modulus of about 200 gigapascals, the relationship between stress and strain is direct and predictable. The total stretch from the hanging weight of the pipe can be calculated precisely if you know the string's cross-section, weight, and length. What makes the calculation complicated in practice is that several forces act simultaneously, each adding or subtracting from the net pipe length, and some of these forces change during the well operations.

Fast Facts

The thermal expansion of production tubing is a well-documented challenge in Canadian oil sands SAGD operations. Cold Lake and Peace River SAGD pairs inject steam at 250 to 300°C. When the tubing is heated from ambient temperature (approximately 5°C surface, 25 to 40°C at reservoir depth) to SAGD operating temperature, the total tubing length can increase by 1.5 to 2.5 metres in a typical 600-metre horizontal well. This elongation must be accommodated by an expansion joint in the tubing string, or the tubing will buckle inside the casing. Expansion joints are a standard component of SAGD completion strings for this reason.

Calculating Pipe Stretch

The stretch from hanging weight alone (the Hooke's Law stretch) is calculated as the integral of the weight below any reference point divided by the pipe's axial stiffness (cross-sectional area times Young's modulus). For a uniform string, this simplifies to:

Stretch = (W × L²) / (2 × A × E)

where W is the weight per unit length of the pipe in air, L is the string length, A is the cross-sectional area of the pipe wall, and E is Young's modulus of steel (approximately 200,000 MPa). In practice, the string is not uniform (it may include drill collars, heavyweight pipe, and different tubing sizes), and the calculation is done numerically section by section.

The pressure stretch (piston effect) depends on where closed-end boundary conditions exist in the string. A packer set in the wellbore creates a closed-end condition: the pressure acting on the pipe cross-section at the packer pushes the tubing upward above the packer (or downward if the string is anchored and the pressure is external). The magnitude of this stretch depends on the area of the restriction and the pressure differential across it.

The ballooning stretch, also called the pressure differential stretch, occurs because internal and external pressure affect the pipe's radial dimensions and, through Poisson's ratio, its axial length. A pipe with higher internal than external pressure tends to barrel out radially and shorten axially (negative stretch). This effect is small per unit length but can accumulate over thousands of metres.

Pipe Stretch in Completions and Perforating

During a perforation job, the wireline tool string is lowered to the correct depth by measuring the cable that has been unreeled from the winch drum. But the cable also stretches under its own weight, and the tool may be in a deviated wellbore where cable depth measurements do not directly translate to tool position along the hole path. To correct for this, wireline operators use a casing collar locator (CCL) to detect the magnetic signatures of each coupling collar on the casing string as the tool passes them. Because the casing was logged after running and before cementing (so the collar positions are known), the CCL signal gives an absolute depth reference that corrects the wireline cable depth for stretch and deviation effects.

When the perforating gun is correlated to the CCL log and the correct collar positions are confirmed, the gun is fired at the depth where the CCL signal matches the pre-perforating plan. Without CCL correlation, pipe stretch errors of 1 to 5 metres are common. In a tight gas well with a 10-metre pay zone, a 3-metre stretch error could result in perforating the cement above the pay zone or missing the perfs entirely.

Pipe stretch is also called string stretch, tubing stretch, or simply stretch in completion engineering. Related terms include Hooke's Law (the principle that the deformation of an elastic body is proportional to the applied force, within the elastic limit; the basis for calculating pipe stretch from tensile load), piston effect (the component of pipe stretch caused by pressure acting on a closed-end area difference in the string, such as a packer or plug; can either elongate or shorten the pipe depending on the direction of the pressure differential), thermal expansion (the increase in length and volume of a material with increasing temperature; a significant contributor to pipe stretch in steam injection and high-temperature wells, calculated using the coefficient of thermal expansion for the specific pipe alloy), casing collar locator (CCL, a wireline tool that detects the magnetic anomaly at each casing collar joint; used to provide absolute depth reference in perforating and other completion operations, correcting for cable stretch and deviation), and neutral point (the point along a drillstring or tubing string where the axial stress transitions from tension above to compression below; the location of the neutral point affects which sections of pipe are in compression and at risk of buckling).

How a Pipe Stretch Error Sent a Packer to the Wrong Zone in a Montney Well

A completions engineer in northeast British Columbia was designing a packer set for a dual-zone Montney well. The lower zone was a 12-metre gas pay between 2,410 and 2,422 metres. The packer needed to set at 2,407 metres, three metres above the top of the lower pay, to isolate it from the upper zone during a sequential fracturing operation.

The engineer calculated pipe stretch using only the Hooke's Law (weight-based) component and did not include the pressure stretch from the 35 MPa wellbore pressure during packer setting. The pressure correction added a further 1.8 metres of stretch at the packer depth. Without this correction, the packer landed at 2,405.2 metres (true position) instead of the intended 2,407 metres, placing it 1.8 metres above the desired landing depth.

During the first fracture stage, pressure built up and the packer failed to isolate the zones properly. Fracture fluid communicated between the two zones, compromising the completion design. A remedial recompletion was required to re-isolate the zones, adding CAD 190,000 to the well cost. The pressure stretch calculation, which takes approximately 30 minutes to add to any packer-setting design, would have prevented the error. It was made a mandatory calculation step in the operator's completion design templates after the incident.