Pore-scale tortuosity models for permeability prediction in subsurface energy systems: A PRISMA-guided systematic review

Tortuosity critically influences permeability and transport in subsurface energy systems, such as geothermal reservoirs, geological CO 2 storage, and underground hydrogen storage, where prediction errors can compromise efficiency and safety. This PRISMA-guided systematic review establishes a decision framework for pore-scale tortuosity studies based on peer-reviewed journals. This study analyzes 30 eligible studies on synthetic media and natural rocks (sandstone, carbonate, shale, coal, and granular materials). Models were classified as empirical, geometric, flow-based, and machine-learning approaches. Quantitative synthesis using a summary estimate plot was performed for reported porosity, tortuosity, and permeability data across methods and lithologies, while reported ARE and AICc values were collated from the literature for a subset of non-machine-learning methods as supporting evidence. A formal meta-analysis was not feasible because most primary studies did not report measures of variance or sample sizes and used heterogeneous definitions of tortuosity. Models incorporating pore connectivity and throat-scale descriptors generally outperform porosity-only formulations. Specifically, semi-empirical formulations incorporating coordination number and throat-scale descriptors reduce the absolute relative error from approximately 124% (Eq. 2, porosity-only) to 12% (Eq. 8, coordination-number-based). In addition, the PSO-SVR machine-learning model achieves RMSE = 0.1376 and R 2 = 0.9694 , while the best CNN reports < 1 % relative error, although direct comparison is subject to differences in reported metrics. The physical and computational assumptions associated with each modeling approach influence its suitability for specific subsurface energy applications, highlighting the importance of application-specific rather than generic model selection.