Thermodynamic Analysis of Thermal Responses in Horizontal Wellbores

Wellbore models are required for integrated reservoir management studies as well as optimization of production operations. Distributed temperature sensing (DTS) is a smart well technology deployed for permanent downhole monitoring. It measures temperature via fiber optic sensors installed along horizontal wellbores. Correct interpretation of DTS surveys has thus become of utmost importance and analytical models for analysis of temperature distribution behavior are critical. In this study, we first show how thermodynamic analysis can describe in detail the physical changes in terms of pressure and temperature behavior from the simplest cases of “leaky tank” to the horizontal wellbore itself. Subsequently, rigorous single-phase thermodynamic models for energy, entropy, and enthalpy changes in horizontal wellbores are derived starting from 1D conservative mass, momentum, and energy balance equations and a generalized thermal models, along with their steady-state temperature profile subsets, are presented. Steady-state applications are presented and discussed. The analysis presents the factors controlling horizontal wellbore steady-state temperature responses and demonstrates that wellbore thermal responses are neither isentropic nor isenthalpic and that the isentropic expansion-driven models and Joule–Thompson-coefficient (JTC) driven may be used interchangeably to analysis horizontal wellbore thermal responses.