Abstract
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.
Highlights
IntroductionFluid particles penetrate pore space and draw paths of various shapes and lengths
The fluid flow through porous media is a complex, multiscale phenomena
The procedure of creating a virtual bed was integrated with scripts in Python programing language, needed for running the YADE code (YADE is a set of libraries which has to be called from an other program - here written in Python), and contains following steps: reading the discrete cumulative curve of the particle distribution; calculating the characteristic lenght with the use of Eq (8); performing Discrete Element Method (DEM) simulations; saving the results; converting the data to the other formats
Summary
Fluid particles penetrate pore space and draw paths of various shapes and lengths. If those paths are short, the drag of porous matrix is relatively low. In order to take this effect into account, Kozeny [24] introduced a new physical quantity named tortuosity. He applied this parameter to correct the value of the hydraulic drop (which in turn depends on the path length) occurring during fluid flow through a porous body (Fig. 1a). The Kozeny formula modified by the Carman is widely known as the Kozeny–Carman equation, which is destined to predict the pressure drop in porous media: dp dx
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