numerical solution. The error in the pressure drop decreases with approximately second order
when refining the mesh (Figure 8). The difference for converged solution with Ergun equation
(24) for coefficients A = 150 and B = 1.75 is found to be 7%. This is quite reasonable agreement
since the considered configuration with given porosity of 40% is a good representaion of the cases
investigated in the experiments by Ergun (1952). It should be noted that for loosely packed beds
with porosity larger than 40% different random configurations may produce different results and
deviations from Ergun values, this is discussed in Freund et al. (2003). In the next section we
show how the local inhomogeneities in the local porosity distribution of randomly packed bed
with the same global parameters (porosity, particle size) may influence the flow and transport
properties.
3.2 Anisotropic effects in fixed beds
It is mentioned in section 1 that Ergun equation (24) is widely used as a drag parametrization
in the coarse grid models. But it includes only averaged properties of the packed bed such as
porosity. Thus, pressure-drop correlations, using only the mean porosity as system describing
parameter, can give an approximate range of the pressure drop in packed beds, but do not
account for the influence of the local structure on the global pressure drop and permeability.
However, in many applications it is important to know how the local anisotropic inhomogeneities
in the packing could affect averaged properties of the packed bed and flow characteristics. These
local inhomogeneities in the granular medium can appear, for example, during dynamic loading
as a result of homogeneous deformation with associative dilatancy or localized shear bands with
even higher void ratios. Anisotropy can be observed also in the improperly fixed packings leading
to the formation of bypass channels. We generate two different configurations of randomly packed
spheres with the same porosity of 42 %. In the first configuration (configuration 1) the anisotropy
in packing in vertical plane is introduced, by removing few particles from initial randomly packed
structure with porosity 36% (Figure 9a). The second configuration (configuration 2) is produced
in the similar way by removing few particles in the horizontal plane (Figure 9b). We estimate the
pressure drop in both anisotropic configurations and compare it with the pressure drop in the
regular random packing with the same porosity of 42%. Figure 10 shows the computed pressure
drop in each configuration. It is found the pressure drop in the configuration 1 is almost identical
to the pressure drop in the regular packing with the same porosity of 36%. The maximum
difference in the pressure drop between these two cases is found to be 22 % (Figure 10). Based
on the averaged packing densities in the granular bed (Figure 11) we represent the packed bed

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