Question

A production tubing string of length 1500 m is tightly held by packers to prevent any expansion in either direction. Production of hot gases from the reservoir increases the temperature of the tubing by 20°C. The Young’s modulus of elasticity of the tubing material is 3000 N/m², and the linear coefficient of thermal expansion is \( 5 \times 10^{-6} \) per °C.
Assuming no radial expansion, and neglecting the weight of the gas in the tubing and its viscosity, the increase in the stress of the tubing due to temperature rise is .......... N/m² (rounded off to two decimal places).

Hint:

When calculating the increase in stress due to temperature rise, remember to use the correct values for Young’s modulus and the coefficient of thermal expansion.

Answer 1

The increase in stress due to temperature rise in the tubing can be calculated using the formula:
\[ \Delta \sigma = E \times \alpha \times \Delta T \] where: - \( \Delta \sigma \) is the increase in stress, - \( E \) is the Young’s modulus of elasticity (3000 N/m²), - \( \alpha \) is the linear coefficient of thermal expansion (\( 5 \times 10^{-6} \) per °C), - \( \Delta T \) is the temperature change (20°C).
Substituting the values:
\[ \Delta \sigma = 3000 \times 5 \times 10^{-6} \times 20 = 0.3 \, {N/m}^2 \] Thus, the increase in stress due to the temperature rise is between 0.28 and 0.32 N/m².