| Abstract |
Fluid flow in geothermal production and injection wells can be strongly affected by heat transfer effects with the formations surrounding the wellbore. Analytical and semi-analytical treatments have been presented in the literature that provide good approximations for the longer-term quasi-steady heat exchange between wellbore fluids and surrounding formations (Ramey, 1962; Wu and Pruess, 1990). These approximations are satisfactory for the long-term behavior of production and injection wells, but they are not able to capture the transient evolution of wellbore heat transmission on time scales from hours to days. Temperature behavior on such time scales plays an important role in the design and analysis of injection tests, as well as for chemical stimulation treatments. This paper presents an adaptation of the well-known semi-analytical heat transfer method of Vinsome and Westerveld (1980) to the problem of heat transfer to and from flowing wells. The Vinsome-Westerveld method treats heat exchange between a reservoir and adjacent cap- and base-rocks by means of a hybrid numerical-analytical method, in which temperature distributions in the conductive domain are approximated by simple trial functions, whose parameters are obtained concurrently with the numerical solution for the flow domain. This method is capable of giving very accurate heat exchange even for non-monotonic temperature variations over a broad range of time scales. The only enhancement needed for applying the method to wellbore heat transmission is taking account of the cylindrical geometry around a flowing well, as opposed to the linear flow geometry in cap- and base-rocks. We describe the generalization of trial functions needed for cylindrical geometry, and present our implementation into the TOUGH2 reservoir simulator. The accuracy of the method is demonstrated through applications to geothermal production and injection problems. |