  Numerical micropermeametry is performed on three dimensional porous samples
having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One
of the samples is a microtomographic image of Fontainebleau sandstone. Two of
the samples are stochastic reconstructions with the same porosity, specific
surface area, and two-point correlation function as the Fontainebleau sample.
The fourth sample is a physical model which mimics the processes of
sedimentation, compaction and diagenesis of Fontainebleau sandstone. The
permeabilities of these samples are determined by numerically solving at low
Reynolds numbers the appropriate Stokes equations in the pore spaces of the
samples. The physical diagenesis model appears to reproduce the permeability of
the real sandstone sample quite accurately, while the permeabilities of the
stochastic reconstructions deviate from the latter by at least an order of
magnitude. This finding confirms earlier qualitative predictions based on local
porosity theory. Two numerical algorithms were used in these simulations. One
is based on the lattice-Boltzmann method, and the other on conventional
finite-difference techniques. The accuracy of these two methods is discussed
and compared, also with experiment.
