When drilling geothermal wells the fluid exchanges thermalenergy to the surrounding rock during its vertical ascenttoward reservoir colder areas. This transmission of heat fromthe casing toward the formation in low permeability reservoirsis essentially conductive. The importance of its study is basedon the fact that this loss of heat could have influence in thenatural fluid thermodynamic conditions and in the predictionof its natural original state. There is even another reason:during drilling, the first thermal data contain valuableinformation about rock thermal parameters, essentiallyeffective thermal conductivity and specific heat. The analysisof the anomalies or discontinuities in the transmission of heatprovide indirect information about the extension andabundance of fractured areas. In this document we present anexact semi-analytic model for the numerical analysis of thetransient heat conduction when the thermal energy flowssimultaneously in radial and vertical directions. This modelprovides a practical solution of the type T (r, z, t) resulting ofcoupling two classic solutions in two independent dimensions.We introduce some applications to a geothermal well in aMexican field.
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