In petroleum engineering practice it is sometimes necessary to predict fluid flow occurring within adjacent regions of porous medium and open space (for example, fractured porous media, 1–3 vuggy media, 4 porous granules5). In such situations the governing flow equations are well known: Darcy's law and the Navier-Stokes equation. However, the set of boundary conditions at the permeable interfaces is seldom obvious. The usual conditions assumed are that the mass flux normal to the surface IS continuous, that the pressure is continuous across the surface, and that the tangential velocity in the free fluid tends to zero at the surface. The first two conditions are completely satisfactory; however, the third is clearly only an approximation. 6