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Hydrocarbon production or fluid injection inevitably involves significant heat exchange between the wellbore fluid and its surroundings. Presence of seawater and air in the riser adds complexity to the heat-transfer process in an offshore environment. During production, the hot fluid continues to lose heat to the increasingly cold surroundings as it ascends the borehole. In contrast, the injected fluid may either gain (cold water) or lose (steam or hot water) heat on descent.

The heat-transfer process just described affects fluid properties and, in turn, the dynamics of fluid flow. Consequently, the coupled nature of momentum and energy transport may require simultaneous solutions for both processes. Whereas steady-state flow modeling is adequate for designing tubular hardware en route to optimal wellhead production, pressure-transient testing may demand rigorous treatment of the coupled and transient nature of momentum, fluid, and heat flows. Similar treatment may be required when shut-in passes are made during production logging runs. This chapter presents a model for estimating the flowing-fluid temperature for the simplest case—that is, when steady-state wellbore fluid and heat flows occur. Chapter 9 discusses transient fluid and heat flow models, followed by their field applications in Chapter 10.

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