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# Mechanical loads on casing and tubing strings

To evaluate a given casing design, a set of loads is necessary. Casing loads result from running the casing, cementing the casing, subsequent drilling operations, production and well workover operations. Mechanical loads are associated with casing hanging weight, shock loads during running, packer loads during production and workovers, and hanger loads.

## Changes in axial load

In tubing and over the free length of the casing above top-of-cement (TOC), changes in temperatures and pressures will have the largest effect on the ballooning and temperature load components. The incremental forces, because of these effects, are given here.

where

Δ*F*_{bal} = incremental force because of ballooning, lbf,

*υ* = Poisson
’
s ratio (0.30 for steel),
*g*_{c} = gravity constant, = 1 lbf/lbm,

Δ*p*_{i} = change in surface internal pressure, psi,

Δ*p*_{o} = change in surface external pressure, psi,

*A*_{i} = cross-sectional area associated with casing inside diameter (ID), in.,

*A*_{o} = cross-sectional area associated with casing outside diameter (OD), in.,

*L* = free length of casing, in.,

Δ*ρ*_{i} = change in internal fluid density, lbm/in.^{3},

and

Δ*ρ*_{o} = change in external fluid density, lbm/in.^{3}.

where

Δ*F*_{temp} = incremental force because of temperature change, lbf,

*α* = thermal expansion coefficient (6.9 × 10^{–6} °F^{–1} for steel), °F^{–1},

*E* = Young
’
s modulus (3.0 × 10 7 psi for steel), psi,
*A*_{s} = cross-sectional area of pipe, in.^{2},

and

Δ*T* = average change in temperature over free length, °F.

## Axial: running in hole

This installation load case represents the maximum axial load that any portion of the **casing** string experiences when running the casing in the hole. It can include effects such as:

- Self-weight
- Buoyancy forces at the end of the pipe and at each cross-sectional area change
- Wellbore deviation
- Bending loads superimposed in dogleg regions
- Shock loads based on an instantaneous deceleration from a maximum velocity [this velocity is often assumed to be 50% greater than the average running speed (typically 2 to 3 ft/sec)]
- Frictional drag (typically, the maximum axial load experienced by any joint in the casing string is the load when the joint is picked up out of the slips after being made up)

## Axial: overpull while running

This installation load case models an incremental axial load applied at the surface while running the pipe in the hole. Casing designed using this load case should be able to withstand an overpull force applied with the shoe at any depth, if the casing becomes stuck while running in the hole. Certain effects must be considered, such as:

- Self-weight
- Buoyancy forces at the end of the pipe and at each cross-sectional area change
- Wellbore deviation
- Bending loads superimposed in dogleg regions
- Frictional drag
- The applied overpull force

## Axial: green cement pressure test

This installation load case models applying surface pressure after bumping the plug during the primary cement job. Because the cement is still in its fluid state, the applied pressure will result in a large piston force at the float collar, and often results in the worst-case surface axial load. The effects that should be considered are:

- Self-weight
- Buoyancy forces at the end of the pipe and at each cross-sectional area change
- Wellbore deviation
- Bending loads superimposed in dogleg regions
- Frictional drag
- Piston force because of differential pressure across float collar

## Axial: other load cases

### Air weight of casing only

This axial load criterion has been used historically, because it is an easy calculation to perform, and it normally results in adequate designs. It still enjoys significant usage in the industry. Because a large number of factors are not considered, it is typically used with a high axial design factor (e.g., 1.6+).

### Buoyed weight plus overpull only

Like the air weight criterion, this load case has wide usage, because it is an easy calculation to perform. Because a large number of factors are not considered, it is typically used with a high axial design factor (e.g., 1.6+).

## Axial: shock loads

Shock loads can occur, if the pipe hits an obstruction or the slips close while the pipe is moving. The maximum additional axial force, because of a sudden deceleration to zero velocity, is given by the equation:

where

*F*_{shock} = shock loading axial force, lbf,

*ν*_{run} = running speed, ft/sec,

*A*_{s} = pipe cross-sectional area, in.^{2},

*E* = Young
’
s modulus for pipe, lbf/in.^{2},
*ρ*_{s} = density of pipe, lbm/ft^{3},

and

*g*_{c} = gravity constant, ft/sec^{2}.

The shock load equation is often expressed as

where *w*_{a} = pipe weight per unit length in air, lbm/ft,

and

*v*_{sonic} = speed of sound in pipe, ft/sec,

= (For steel, *v*_{sonic} is 16,800 ft/sec.)

For practical purposes, some operators specify an average velocity in this equation and multiply the result by a factor that represents the ratio between the peak and average velocities (typically 1.5).

## Axial: service loads

For most wells, installation loads will control axial design. However, in wells with uncemented sections of casing, and where large pressure or temperature changes will occur after the casing is cemented in place, changes in the axial load distribution can be important because of effects such as:

- Self-weight
- Buoyancy forces
- Wellbore deviation
- Bending loads
- Changes in internal or external pressure (ballooning)
- Temperature changes
- Buckling

## Axial: bending loads

Stress at the pipe ’ s OD because of bending can be expressed as ....................(5)

where

*σ*_{b} = stress at the pipe
’
s outer surface, psi,
*E* = modulus of elasticity, psi,

*D* = nominal outside diameter, in.,

and

*R* = radius of curvature, in.

This bending stress can be expressed as an equivalent axial force as

where

*F*_{bnd} = axial force because of bending, lbf,

*α/L* = dogleg severity (°/unit length),

and

*A*_{s} = cross-sectional area, in^{2}.

The bending load is superimposed on the axial load distribution as a local effect.

## Sample uniaxal tension calculation

For this example, consider a 9 ^{5}/_{8}-in. 43.5-lbm/ft N-80 production casing in an 11,000-ft vertical well, with TOC at 8,000 ft. The casing is run in 11-lbm/gal water-based mud. The hanging weight in air for the casing is

The casing stress at the surface is *F*_{air} divided by the cross-sectional area of the casing, less the hydrostatic pressure at the bottom of the casing when cemented. If we assume 15-lbm/gal cement and 11-lbm/gal displaced mud, this bottomhole pressure is

Therefore, the surface hanging stress is

For N-80 casing, a stress of 31,181 psi leaves a large margin of safety. Next, consider the effects of a stimulation treatment on this surface stress. Assume that the average temperature change in the 0–8,000-ft interval is –50°F. The change in axial stress, because of this temperature increase, is given by **Eq. 2**.

where *α* is the coefficient of thermal expansion (6.9 × 10 6 /°F for steel) and *E* is Young
’
s modulus (30 × 10^{6}psi for steel). The net surface stress in the casing is

## References

## See also

External pressure loads on casing and tubing strings

Internal pressure loads on casing and tubing strings

Thermal loads on casing and tubing strings

## Noteworthy papers in OnePetro

## External links

## General references

Brand, P.R., Whitney, W.S., and Lewis, D.B. 1995. Load and Resistance Factor Design Case Histories. Presented at the Offshore Technology Conference, Houston, 1-4 May. OTC-7937-MS. http://dx.doi.org/10.4043/7937-MS.

Galambos, T.V., Ellingwood, B., MacGregor, J.G. et al. 1982. Probability-based Load Criteria: Assessment of Current Design Practice. *J. of the Structural Division*, ASCE, **108** (5): 959-977.

Hammerlindl, D.J. 1977. Movement, Forces, and Stresses Associated With Combination Tubing Strings Sealed in Packers. *J Pet Technol* **29** (2): 195–208; Trans., AIME, 263. SPE-5143-PA. http://dx.doi.org/10.2118/5143-PA.

Klementich, E.F. and Jellison, M.J. 1986. A Service-Life Model for Casing Strings. *SPE Drill Eng* **1** (2): 141-152. SPE-12361-PA. http://dx.doi.org/10.2118/12361-PA.

Lewis, D.B., Brand, P.R., Whitney, W.S. et al. 1995. Load and Resistance Factor Design for Oil Country Tubular Good. Presented at the Offshore Technology Conference, Houston, 1-4 May. OTC-7936-MS. http://dx.doi.org/10.4043/7936-MS.

*Load and Resistance Factor Design Specification for Structural Steel Buildings*. 1986. Chicago: American Institute of Steel Construction.

*Minimum Design Loads for Buildings and Other Structures, ANSI A58.1-82*. 1982. New York City: American National Standards Institute.

Mitchell, R.F.: “Casing Design,” in Drilling Engineering, ed. R. F. Mitchell, vol. 2 of Petroleum Engineering Handbook, ed. L. W. Lake. (USA: Society of Petroleum Engineers, 2006). 287-342.

Prentice, C.M. 1970. "Maximum Load" Casing Design. *J. Pet Tech* **22** (7): 805-811. SPE-2560-PA. http://dx.doi.org/10.2118/2560-PA.

Rackvitz, R. and Fiessler, B. 1978. Structural Reliability Under Combined Random Load Processes. *Computers and Structures* **9:** 489.