A Comprehensive Simplified Algorithm for Heat Transfer Modeling of Medium-Deep Borehole Heat Exchangers Considering Soil Stratification and Geothermal Gradient

Medium-deep borehole heat exchanger (BHE) systems represent an emerging form of ground source heat pump technology. Their heat transfer process is significantly influenced by geothermal gradient and soil stratification, typically simulated using segmented finite line source (SFLS) models. However, this approach involves computationally intensive procedures that hinder practical engineering implementation. Building upon an SFLS model adapted for complex geological conditions, this study proposes a comprehensive simplified algorithm: (1) For soil stratification: A geothermally-weighted thermal conductivity method converts layered heterogeneous media into an equivalent homogeneous medium; (2) For geothermal gradient: A temperature correction method establishes fluid temperatures under geothermal gradient by superimposing correction terms onto uniform-temperature model results (g-function model). Validated through two engineering case studies, this integrated algorithm provides a straightforward technical tool for heat transfer calculations in BHE systems.