We Study the periods that develop in the drying of capillary Porous media, particularly the constant rate (CRP) and the falling rate (FRP) periods. Drying is simulated with a 3-D pore-network model that accounts for the effect of capillarity and buoyancy at the liquid-gas interface and for diffusion through the porous material and through a boundary layer over the external surface of the material. We focus on the stabilizing or destabilizing effects of gravity on the shape of the drying curve and the relative extent of the various drying periods. The extents of CRP and FRP are directly associated with various transition points of: the percolation theory, such as the breakthrough point and the main liquid cluster disconnection point. Our study demonstrates that when an external diffusive layer is present, the constant rate period is longer. (c) 2005 Elsevier Inc. All rights reserved.