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Open Access Publications from the University of California

A Hybrid Semi-Analytical and Numerical Method for Modeling Wellbore Heat Transmission


Fluid flow in geothermal production and injection wells can be strongly affected by heat transfer effects with the formations surrounding the wellbore. Various techniques and approximations to model wellbore heat transmission have been presented in the literature. The objective of the present work is to develop a treatment of conductive heat transfer in the formations surrounding a wellbore that is simple, yet provides good accuracy for transient effects at early time. This is accomplished by adapting the well known semi-analytical heat transfer method of Vinsome and Westerveld (1980) to the problem of heat transfer to and from a flowing well. 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 can give a very accurate representation of conductive heat transfer 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 evaluated through application to non-isothermal flow through a pipe.

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