Entransy-energy synergistic optimisation of thermodynamic performance in two-stage cascaded phase change materials for backfill body geothermal system

Cascaded latent heat storage technology has emerged as an effective strategy to enhance the stability and efficiency of geothermal storage systems by utilising latent heat release of phase change materials (PCMs) at specific temperatures. In this study, a novel backfill body cascaded latent heat storage geothermal utilisation (BCLHSGU) system was developed, using three paraffin wax types with distinct melting points as the backfill PCM. Heat release process of this system was simulated using ANSYS Fluent software. First, heat transfer performance along the paths of both single-stage and two-stage systems was comprehensively analysed. Next, thermodynamic performance of each phase change unit within the two-stage system was examined under varying operating conditions by adjusting inlet temperature and working fluid (WF) flow rate. Heat release performance of the two-stage system was further investigated through a synergistic entransy-energy analysis and sensitivity analysis, focusing on quantifying the influence of key factors on the heat release process. Finally, the impact of additional phase change stages on the overall heat release performance was thoroughly evaluated. Results revealed that the two-stage system exhibited a 14.15% reduction in heat release time compared to the single-stage system, with superior uniformity in heat transfer temperature differences along the path. By lowering WF inlet temperature, heat release efficiency and entransy efficiency of the two-stage system were enhanced by 9.51% and 9.5%, respectively, although entransy dissipation increased by 6.76%. Conversely, increasing the inlet flow rate of the WF led to significant improvements in heat release efficiency and entransy efficiency, by 31.59% and 31.31%, respectively, while dramatically reducing the entransy dissipation by 71.88%. Additionally, the sensitivity coefficient of WF inlet temperature to energy and entransy gains was nearly two orders of magnitude higher than WF inlet velocity. When compared to the two-stage system, the three-stage system did not show any major improvement in heat release performance. Instead, it led to increased system dissipation during the later heat release period. A novel entransy–energy synergistic analysis framework developed in this study effectively addresses the critical trade-off between heat extraction efficiency and dissipation within the BCLHSGU system. These findings provide a reference for the efficient heat extraction of the backfill body latent heat storage energy system (BLHESS).