  Permeability is the key parameter for quantifying fluid flow in porous rocks.
Knowledge of the spatial distribution of the connected pore space allows, in
principle, to predict the permeability of a rock sample. However, limitations
in feature resolution and approximations at microscopic scales have so far
precluded systematic upscaling of permeability predictions. Here, we report
fluid flow simulations in capillary network representations designed to
overcome such limitations. Performed with an unprecedented level of accuracy in
geometric approximation at microscale, the pore scale flow simulations predict
experimental permeabilities measured at lab scale in the same rock sample
without the need for calibration or correction. By applying the method to a
broader class of representative geological samples, with permeability values
covering two orders of magnitude, we obtain scaling relationships that reveal
how mesoscale permeability emerges from microscopic capillary diameter and
fluid velocity distributions.
