Safety limit of super-long inner pipe in coaxial borehole: A thermal-hydraulic-mechanical coupled algorithm

Medium-deep coaxial borehole heat exchangers are important in decarbonizing heating systems. However, the design of super-long inner pipes, governing system's safety and efficiency, remains a challenge. Current designs lack theoretical foundations due to variable thermal-hydraulic-mechanical multi-physics interactions and insufficient characterization of external pressure resistance, leading to recurrent inner pipe failures. Therefore, we conducted full-scale external pressure and tensile tests based on actual temperature-pressure conditions and developed an inner pipe design algorithm that couples thermal, hydraulics, tensile forces and two-dimensional strength. Results show temperature increase reduces the strength of PE-RT II pipes; borehole top is weak point for external pressure while bottom is vulnerable to tensile; formation temperature is the dominant factor affecting safety limit. Engineer-ready design charts considering design factors show flow-pressure-depth limits across geological scenarios. They show that flow limits decrease with depth at a reducing rate and pressure limits show a similar but more linear decreasing trend. By comparison analysis, Φ110 × 12.3 mm PE-RT II pipe demonstrates the highest pressure and limits. Maximum heat extraction capacity follows an S-shaped curve with depth, with greater performance differences between pipe sizes at larger depths. This work provides actionable guidelines for ground heat exchanger design and standardization to avoid risks.