  The estimation of the permeability of porous media to fluids is of
fundamental importance in fields as diverse as oil and gas industry,
agriculture, hydrology and medicine. Despite more than 150 years since the
publication of Darcy's linear law for flow in porous media, several questions
remain regarding the range of validity of this law, the constancy of the
permeability coefficient and how to define the transition from Darcy flow to
other flow regimes. This study is a numerical investigation of the permeability
and flow stability in a nonrandom quasi-tridimensional porous medium analog.
The effect of increasing pressure gradient on the velocity field and on the
estimation of Darcy and Darcy-Forchheimer coefficients is investigated for
three different obstacle's radiuses. The transition from Darcy flow to
nonlinear behavior is associated with the formation of jets in the outlet of
the porous medium and development of flow instabilities. Different
representations of the Reynolds number proved adequate to detect deviation from
the linear law. The instantaneous permeability calculated at each pressure
gradient was sensitive to flow velocity, in agreement with previous studies
stating that permeability cannot be conceptualized as a constant for real
flows.
