An analytical model for predicting outlet fluid temperatures in energy piles using soil thermal resistances

Predicting outlet fluid temperatures of energy piles during the preliminary design phase is important for estimating their geothermal potential. However, this stage is often constrained by incomplete design information and limited computational resources. This paper presents a simplified analytical model to estimate outlet fluid temperatures and heat exchange rates for single energy piles. The model is particularly suited for preliminary design stages, offering an alternative to complex numerical solutions that require extensive computational effort. The model assumes the energy pile as a line heat source installed in thermally homogenous soil. It uses the following basic input parameters: inlet fluid temperatures, flow rates, pile lengths, effective soil thermal resistances, and initial soil temperatures. The model's accuracy was verified against several field tests conducted under a variety of boundary conditions. The field validations demonstrate the model's applicability under diverse conditions, including monotonic and cyclic temperature variations, varying pile dimensions, head loads, heat exchanger pipe configurations and quantities, flow rates, timeframes, soil profiles, and group effects, with most tests showing errors within 2 °C. Additionally, a year-long predictive analysis of a single energy pile showed that the model's simulated heat exchange rates aligned well with expected ranges for energy piles. These results confirm the model's reliability and practical utility in preliminary energy pile design.