Helical Path Tortuosity Model for Sandstone Formations: A Unified Approach Across Permeability Ranges

This study develops a helical path tortuosity model with formation-specific parameterization to address the critical limitation of existing tortuosity models that typically excel within narrow permeability ranges. The model decomposes total tortuosity into three physically meaningful components: geometric tortuosity arising from flow path winding, constriction effects from pore throat narrowing, and percolation factors reflecting connectivity limitations. We implemented formation-specific critical porosity thresholds (ϕ₀) calibrated to unique connectivity characteristics of different sandstone classes. The model was validated across an extensive dataset spanning five orders of magnitude in permeability (0.00006–36 μm²), encompassing tight German sandstones, clean Fontainebleau quartz arenites, and unconsolidated high-connectivity formations. Formation-specific parameterization significantly improved predictive performance compared to the global model, with R² increasing from 0.77 (global) to 0.89–0.97 (formation-specific) and MAPE decreasing from 10.11% to 2.46%–4.40%. Quantitative component contribution analysis revealed that while geometric tortuosity dominates across all formation types (70%–77%), the relative importance of constriction and percolation effects varies systematically with formation characteristics. The model establishes formation-specific parameter scaling relationships that provide deeper insights into the fundamental physics governing fluid transport across different sandstone classes. This unified approach bridges critical gaps in our ability to predict tortuosity across the full spectrum of sandstone formations encountered in geological systems.