A spatiotemporal decoupling and dimensionality reduction algorithm for numerical simulation of multiple deep borehole heat exchangers based on alternating direction implicit method

The coaxial deep borehole heat exchanger (C-DBHE) is a critical component for deep geothermal development. Multiple coaxial deep borehole heat exchangers (C-DBHEs) are typically deployed to meet high heat extraction demands in practical engineering applications. However, the prohibitively high computational cost of numerical simulations remains a major challenge for modeling C-DBHEs. To address this issue, this study proposes an efficient numerical algorithm based on spatiotemporal decoupling and dimensionality reduction. The key innovation is the synergistic integration of the alternating direction implicit method with explicit heat source treatment, which transforms the three-dimensional problem into a series of one-dimensional calculations, enabling rapid simulations previously unattainable with conventional methods. The reliability of the model algorithm is validated through mesh independence tests, comparisons with literature results, and field measurements. Results demonstrate that the algorithm significantly enhances computational efficiency while maintaining acceptable accuracy. Specifically, a 20-year simulation for a three-borehole configuration can be completed in just 2030 s on a personal computer. Simulations of various C-DBHEs configurations reveal that thermal interference intensifies with increasing borehole cluster size and operation duration. Heat extraction performance of the central borehole in C-DBHEs showing the most significant decline. This study provides an efficient and reliable simulation tool for the design, optimization, and long-term performance assessment of large-scale deep geothermal systems.