  In this paper we study stationary incompressible Newtonian fluid flow in a
thin porous media. The media under consideration is a bounded perforated $3D$
domain confined between two parallel plates. The description of the domain
includes two small parameters: $\varepsilon$ representing the distance between
pates and $a_\varepsilon$ connected to the microstructure of the domain such
that $a_\varepsilon\ll \varepsilon$. We consider the classical setting of
perforated media, i.e. $a_\varepsilon$-periodically distributed solid (not
connected) obstacles of size $a_\varepsilon$. The goal of this paper is to
introduce a version of the unfolding method, depending on both parameters
$\varepsilon$ and $a_\varepsilon$, and then to derive the corresponding $2D$
Darcy's law.
