The Path Tracking Method as an alternative for tortuosity determination in granular beds

Tortuosity is one of the most elusive parameters of porous media. The fundamental question is whether it may be computed from the geometry only or the transport equations must be solved first. Elimination of the transport equations would significantly decrease the computation time and memory consumption and thus allow investigating larger samples. We compare the geometric to hydraulic tortuosity of a sphere-packed porous media. We applied the Discrete Element Method to generate a set of virtual beds based on experimental data taking into account the real porosity and particle distribution, the Lattice Boltzmann Method to compute the hydraulic tortuosity and geometrical approach, i.e. so-called Path Tracking Method, to calculate the geometrical tortuosity. Our study shows that the calculation time can be reduced from hours (if the LBM is used) to seconds (if the PTM is applied) without losing the accuracy of the final results. The relative error between average values of the tortuosity obtained for both used methods is less than 3%. We show that the applied geometrical method may serve as an attractive alternative to hydraulic tortuosity, particularly in large granular systems.