Exploring alteration of near-wellbore geothermal gradient during fluid circulation and production

The constant undisturbed formation temperature profile controlling heat transfer into the wellbore appears counterintuitive in light of transient cooling of the formation that occurs upon fluid circulation in drilling and also heating during fluid production. This study presents a mathematical model that shows that the heat transfer occurs from the wellbore/formation interface, not from some distance away from the wellbore wherein the initial formation temperature profile remains undisturbed. This new model allows investigation of heat transfer behavior from the formation into the wellbore during drilling or fluid circulation, and from the wellbore into the reservoir in the production mode. Application of the line-source solution for the temperature diffusivity equation for a steady-state system provides the necessary ingredients for computing the temperature behaviors at different times and radii. This line-source solution can be used throughout the wellbore to determine the undisturbed formation temperature, which may be used to obtain the geothermal gradient dependent on the radius and fluid circulation time. Therefore, the initial geothermal gradient works as a time-dependent variable, and the resultant second-order polynomial relationships can describe the undisturbed formation temperature. This study provides the required tools to assess the wellbore heat-transfer behavior and their effect on the wellbore temperature profiles. Also, the new mathematical model illuminates the impact of heat transfer by comparing its performance with the original formulations. Besides, this paper presents a complete derivation of the line-source solution of the temperature diffusivity equation to justify the proposed approach.