  For a fully-coupled Darcy-Stokes system describing the exchange of fluid and
stress balance across the interface between a saturated porous medium and an
open very narrow channel, the limiting problem is characterized as the width of
the channel converges to zero. It is proven that the limit problem is a
fully-coupled system of Darcy flow in the porous medium with Brinkman flow in
tangential coordinates of the lower dimensional interface.
