This paper presents a general and unified equation for flowing temperature prediction that is applicable for the entire range of inclination angles. The equation degenerates into Ramey's equations for ideal gas or incompressible liquid and into the Coulter and Bardon equation, with the appropriate assumptions. This work also proposes an approximate method for calculating the Joule-Thomson coefficient for black-oil models.
Flowing temperature distribution often is predicted with different methods for pipelines and wellbores. The Ramey method usually is used for predicting wellbore temperature distribution. This method rigorously incorporates the complex process of transient heat transfer between the wellbore and the reservoir. Ramey's method, however, is limited to either ideal gas or incompressible liquid flow. The Coulter and Bardon equation commonly is used for pipeline temperature prediction. A more rigorous thermodynamic behavior of the flowing fluid is taken into account, incorporating the Joule-Thomson coefficient. Although the Coulter and Bardon equation originally was derived for gas flow, it also is used for single-phase liquid or two-phase flow. This equation is limited, however, by the assumptions of steady-state heat transfer with a constant-temperature environment and horizontal flow.