A Generalized Analytical Heat Transfer Model for Enhanced Geothermal Systems: Capturing Fracture Interactions and Correcting Classical Optimistic Predictions

Abstract

Numerical analytical heat transfer models play a critical role in geothermal design and feasibility studies. Classical solutions, such as those proposed by Gringarten et al. 1975, rely on simplified assumptions and systematically overestimate thermal performance, which can lead to unrealistic engineering decisions. This study presents a generalized analytical model for enhanced geothermal systems that explicitly captures thermal interactions between fractures while preserving analytical tractability. The formulation is based on Green\'s functions and reproduces realistic thermal behavior under conditions representative of fractured geothermal reservoirs. The resulting solution is computationally efficient and sufficiently simple to be implemented directly in standard spreadsheets, without requiring Laplace space transformations or numerical inversion algorithms. The model is validated against numerical simulations performed using CMG STARS and Volsung software, showing close agreement in temperature evolution, including the effects of interacting fractures. Compared with classical analytical approaches, the proposed model corrects optimistic bias and provides more reliable predictions of production temperature and energy recovery. These results have direct implications for geothermal feasibility studies, well design, and power forecasting, effectively bridging the gap between legacy analytical models and numerical or commercial engineering tools. Building on the analytical framework originally introduced by Gringarten et al. 1975, the proposed formulation generalizes classical heat transfer solutions to account for fracture interaction while retaining analytical simplicity and practical applicability.