Tortuosity of the medium

In the porous medium, diffusion is affected by the porosity and tortuosity of the medium itself therefore Knudsen diffusion is computed as well as the ordinary diffusion. Eventually, an effective diffusion coefficient is calculated that depends on the ordinary and Knudsen diffusion coefficients and on the ratio between porosity and tortuosity of the medium (Equation (3.58)). 

These descriptions apply to diffusion processes inside a pore, but on a longer time scale (interpore regime), the diffusion of solutes will be controlled by the shape of the porous network itself (which can be treated as a Knudsen diffusion regime). The description of Knudsen diffusion is beyond the scope of this paper, but we can recollect that the tortuosity of the medium, besides the pore diameter, is an important parameter that can slow down interpore diffusion and hence diffusion-controlled reactions. ... 

A capillary tube model can be used to estimate the permeability of the medium before fines deposition or release has occurred. The Car-man-Kozeny equation uses the diameter of the substrate particles, dg, and the tortuosity of the medium, r, to evaluate the effective permeability of the porous medium. 

Here, r, cj), and r are the mean radius of the pores and the porosity and tortuosity of the medium, respectively. 

Tortuosity is defined as the relative average length of a flow path (i.e., the average length of the flow paths to the length of the medium). It is a macroscopic measure of both the sinuosity of the flow path and the variation in pore size along the flow... 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

Mixing Due to Obstructions The tortuosity of the flow channels in a porous medium means that fluid elements starting a given distance from each oilier and proceeding at the same velocity will not reniain tlie same distance apart. 

Tortuosity factor The distance a particle must travel to pass through a porous medium divided by the overall length of the medium. 

A similar process will occur in a static fluid in a porous medium. The diffusion process in this case will be hindered by the presence of the solid phase. The cross sectional area across which diffusion can take place is reduced by a factor that is equal to the volumetric water content, 6. The tortuosity of the pores increases the microscopic distance across which... 

Characterization of porous media based on the pore (microscopic) level is carried out for the purpose of understanding, modeling, and sometimes controling the macroscopic behavior and properties of the medium. The macroscopic (bulk) properties needed to relate to the pore description are porosity, permeability, tortuosity, and connectivity. When one examines a sample of a porous medium, for example, sandstone, it is obvious that the number of pore sizes, shapes, orientations, and interconnections is enormous. Furthermore, even the identification of a pore is not unique. Because of this complexity, pore structure is often characterized based on an idealized model. A true description is not realistic for a natural porous medium. 

Equation 71 is the basic equation that relates permeability of a porous medium to its other properties. However, equation 71 contains the hydraulic diameter of the passage (pore), tortuosity, and areal porosity of the medium, which may not be easily accessible. For example, sandstones or rock formations have irregular pore structure and often have inconsistent pore size measurement values (see previous section). It is rather difficult to measure the average hydraulic pore diameter. On the other... 

In this equation, d is the tortuosity of the porous medium (between 0 and 1 0.5 would be typical for a consolidated sandstone), Z>nuid is the diffusion coefficient in pure fluid and i is a retardation factor, defined as... 

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