Heat transfer during two-phase flow in wellbores. Part I. Formation temperature
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abstract
Heat loss from the wellbore fluid depends on the temperature distribution in the formation. Formation temperature distribution around a well was modeled by Ramey (1962) by assuming a vanishingly small wellbore radius. The assumption, while robust for some cases, could lead to unrealistic predictions of early-time behavior. This paper uses a rigorous model of heat transfer developed with consideration for the appropriate boundary conditions; that is, the heat transfer at the formation/wellbore interface is represented by the Fourier law of heat conduction. The superposition principle is used to account for the gradual change in heat transfer rate between the wellbore and the formation. The results of the new analysis are in agreement with the classical work of Ramey for large times (dimensionless time, tD > 10). However, significant differences are noted between the proposed solution and that of Ramey's log-linear approximation at small (tD < 1.0) times. These differences may have considerable effect on certain applications, such as static earth temperature estimation from temperature logs, and bottomhole temperature estimation for cyclic steam injection. We also present an approximate algebraic expression for the rigorous integral solution of dimensionless formation temperature, TD. This simplified expression is accurate for most engineering calculations. Use of this solution is shown in the second part of the paper where the wellbore fluid temperature distribution is computed during two-phase flow.
