Stochastic tortuosity

Apparently the parameters of stochastic models are quite different from those of classic (deterministic) models where the permeability, the porosity, the pore radius, the tortuosity coefficient, the specific surface, and the coefficient of the effective diffusion of species represent the most used parameters for porous media characterization. Here, we will present the correspondence between the stochastic and deterministic parameters of a specified process, which has been modelled with a stochastic and deterministic model in some specific situations. 

A.N. Patwardhan and R. Mann, Effective diffusivity and tortuosity in Wicke-Kallenbach experiments Direct interpretation using stochastic pore networks, Trans. /. Chem, E. 691A),205 (1991). 

Summarizing, this peper has presented a method to study scale up processes (mesoscale to core scale) of flow in perous media from geometry, fluid parameters, stochastic realization and LBM namely, pwameters such as tortuosity (arbitrarily generated p>orous media always have a clearly smaller tortuosity than randomly generated pwrous media), randomness in void space, geometrical distribution, porosity and consistency index of the non-Newtonian fluid, among others. This model is ready to predict as an output from thin small samples, effective p>ermeabihty bands and the corresponding subsurface probability distributions scaled up for subsurface reservoirs, aquifers, etc. 

Several stochastic models have been developed to reconstract the GDL microstructure. With a reconstracted GDL, Wang etal [34] further presented a detailed DNS study to investigate the transport phenomena of mass, reactant, electron, and heat inside a GDL. In this approach, the Navier-Stokes equation was apphed directly to the void space with no slip boundary condition at the sohd matrix surface. The oxygen and water transport can be expressed in a similar way to that in the DNS of CLs. Figure 30.8 shows the mass flow through the microstructure of the GDL. The results were used to evaluate the GDL properties, such as the permeabihty and tortuosity. They found that the tortuosity of the considered pore structure is 1.2 whereas the permeability fC is 3.1 x 10 m [34]. 

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