Temperature and Heat Transfer Along Buried Liquids Pipelines
Authors: Hooker P.R. , Brigham W.E. 
Published: December 2007

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Evaluating the heat generated and transferred by buried liquids pipelines usually has been important only in special circumstances, such as the Trans-Alaska pipeline. The published equations for calculating this temperature and heat transfer in such pipelines are misleading. These equations predict the "frictional heating" in liquids pipelines, but are valid only for liquids with a negligible pipelines, but are valid only for liquids with a negligible coefficient of thermal expansion. The actual change in temperature is caused by heat transfer and the Joule-Thomson coefficient. In this study, we discuss the difference between the frictional-heating and Joule-Thomson coeffecient equations, present an example for an adiabatic pipeline, and develop a model for steady-state heat pipeline, and develop a model for steady-state heat transfer to or from a buried pipeline. When deriving the model, we assumed that the coefficient of thermal expansion and the specific volume of the fluid are almost constant for the range of working temperatures and pressures. The soil is assumed to be homogeneous with a pressures. The soil is assumed to be homogeneous with a constant thermal conductivity, kh, and a constant effective surface temperature, Ts. We also assumed the film coefficient of the fluid on the pipe wall is negligible and that the thermal conductivity of the pipe is infinite. Even with these assumptions, a good, quick engineering approximation of the temperature change in a buried liquids pipeline system may be determined using these equations.
The equation for the infinitesimal changes in temperature for pure substances for any process between equilibrium states is developed in most thermodynamic texts and any be expressed as (1)
For an adiabatic pipeline (where dh=0) in which the isobaric thermal expansion of the fluid, (delta v/delta T), is negligible, Eq. 1 may be simplified to (2)
This is the equation commonly seen for friction heating. Katz shows that the frictional pressure-loss equation may be written as (3)
Katz then relates Eqs. 2 and 3 to predict the temperature rise that occurs as liquid flows through an adiabatic pipeline: pipeline: (4)
Integrating Eq. 4 over the length of the pipeline, L, with inlet temperature, T, and outlet temperature, T, yields
(5)
However, Eq. 5 is not correct for most liquids. Instead, the Joule-Thomson coefficients must be used as indicated below. (6)
Note that this is this coefficient of the right-hand term in Eq.1.
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