Abstract
The article proposes functions linking the standard deviation of a particle distribution in a porous bed consisting of spherical particles with various parameters characterising the spatial structure of the bed. The porosity, the inner surface, the specific surface and the geometrical tortuosity were analysed. In the first stage, a set of virtual beds was created with the use of the Discrete Element Method. The Radius Expansion Method was applied to generate virtual beds with different standard deviations. 150 virtual beds were created (25 standard deviations, 3 repetitions with different settings of the random number generator, 2 values of the radius expansion factor). In the second stage, the spatial structure of all virtual beds was analysed. The geometrical tortuosity was calculated with the use of the so-called Path Tracking Method; other parameters were calculated with the use of analytical formulas. The impact of the standard deviation on the parameters characterising the spatial structure of the granular bed was described by approximation functions, which can be used in order to obtain these parameters based on the particle size distribution for others porous beds.
Highlights
The prediction of the pressure drop, occurring during fluid flows through porous media, is one of the most important problems in the widely understood science and engineering
The following conclusions can be formulated based on the above-discussed topics: (1) Geometrical parameters characterising granular beds may be treated as functions of the standard deviation of the particle distribution
These functions may be obtained on the basis of Discrete Element Method and statististical methods; (2) The obtained functions may be used as replacements of constant values in such formulas like e.g. Kozeny–Carman equation, in which the porosity, the tortuosity factor and the specific surface have to be stated; (3) The functions proposed in the paper are developed on the basis of virtual beds and may be treated only as an estimation
Summary
The prediction of the pressure drop, occurring during fluid flows through porous media, is one of the most important problems in the widely understood science and engineering. This issue plays significant role in geology, civil engineering, agriculture, food industry, chemistry and many other areas. Besides Darcy [11], achievements of Hazen [19], Slichter [35], Terzhagi [44], Kozeny [22] or Carman [6] must be mentioned here Detailed review of these formulas is not important in the context of this article (it can be found e.g. in [41]). The crucial thing is that all these formulas are functions of different parameters characterising the geometrical
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