  We study numerically the tortuosity--porosity relation in a microscopic model
of a porous medium arranged as a collectin of freely overlapping squares. It is
demonstrated that the finite-size effects and the discretization errors, which
were ignored in previous studies, may cause significant underestimation of
tortuosity. The simple tortuosity calculation method proposed here eliminates
the need for using complicated, weighted averages. The numerical results
presented here are in good agreement with an empirical relation between
tortuosity ($T$) and porosity ($\phi$) given by $T-1\propto \ln\phi$, that was
found by others experimentally in granule packings and sediments. This relation
can be also written as $T-1\propto R S/\phi$ with $R$ and $S$ denoting the
hydraulic radius of granules and the specific surface area, respectively.
