Difference in temperature causes steel to contract or expand. If tubing is __free to move__, length of the tubing will be either longer or shorter due to thermal expansion. On the other hand, if the tubing is not free to move, there will be a change in axial force due to the temperature effect.

Figure 1 illustrates an increase in length due to heat and Figure 2 demonstrates a decrease in length because of cooling.

Magnitude of contraction or expansion force is dependent on expansion coefficient of steel (Ct).

**If tubing is anchored**, the force generated by temperature change is calculated by the following equation.

Where;

F_{TEMP} = Force generated by change in temperature (inch)

C_{T} = Thermal expansion coefficient (1/F)

E = Young’s Modulus of material (psi)

ΔT = Average temperature change from the initial condition to the final condition

As = Cross sectional area of tubular (inch^{2})

Average Temperature = (Surface Temperature + Bottom Hole Temperature) ÷2 (F)

**If tubing is free to move**, the force generated by temperature change is calculated by the following equation.

Where;

ΔL_{TEMP }= Length change due to thermal effect (inch)

C_{T} = Thermal expansion coefficient (1/F)

L = Length of tubing (inch)

ΔT = Average temperature change from the initial condition to the final condition (F)

Average Temperature = (Surface Temperature + Bottom Hole Temperature) ÷2 (F)

Thermal changes can happen during the life of the well. While producing, heat from the reservoir will expand the length of the tubing, whereas an injection operation will contract tubular due to cooling down the temperature. Figure 3 shows the difference in temperature gradient while the well is on production or injection. Therefore, it is important to understand how thermal will affect changes in length or force in the tubular.

**Example – **This example will demonstrate how to calculate a length change due to thermal effect.

Tubing is free to move.

Packer setting depth is 10,000 ft.

C_{T} = 6.9×10^{-6 }(1/F)

**At the initial condition**

Surface temperature (F) = 60F

Bottom hole temperature (F) = 150 F

**At the final condition**

Surface temperature (F) = 90F

Bottom hole temperature (F) = 150 F

**Solution**

Length of tubing (inch) 12 × 10,000 = 120,000 inch

Average Temperature at Initial Condition = (60 + 150) ÷2 = 105 F

Average Temperature at Final Condition = (90 + 150) ÷2 = 120 F

ΔT = 120 – 105 = 15 F

ΔL_{TEMP }= 12.42 inch

**Conclusion**

Length of tubular will increase by 12.42 inches due to thermal affect based on the given information.

**References**

Jonathan Bellarby, 2009. *Well Completion Design, Volume 56 (Developments in Petroleum Science)*. 1 Edition. Elsevier Science.

Wan Renpu, 2011. *Advanced Well Completion Engineering, Third Edition*. 3 Edition. Gulf Professional Publishing.

Ted G. Byrom, 2014. *Casing and Liners for Drilling and Completion, Second Edition: Design and Application (Gulf Drilling Guides)*. 2 Edition. Gulf Professional Publishing.

Lubinski, A., & Althouse, W. S. (1962, June 1). Helical Buckling of Tubing Sealed in Packers. Society of Petroleum Engineers. doi:10.2118/178-PA

Thank you for a good explaination.

Only one thing you forget is the equation in case free movement pipe or anchored pipe.

Moh,

This issue is fixed.

Thanks for information.

Regards,

Shyne

Thank you Shyne. Just one point to be considered for anchored tubing. The equation for the force should be without “E” (Young Modulus), Thanks again for a good Website.

I will add more details later.

Dear sir,

Thanks a lot for useful articles.

There aren’t the formula for two conditions in this article.

If possible, please add one example for anchored tubing.

Regards,

Reza