The phenomena occurring at the surface of a porous medium during drying in the capillary regime are investigated by pore network simulations. The impact of the formation of wet and dry patches at the surface on the drying rate is studied. The simulations indicate an edge effect characterized by a noticeable variation of saturation in a thin layer adjacent to the porous surface. Also, the results indicate a significant nonlocal equilibrium effect at the surface. The simulation results are exploited to test Schlunder's classical model which offers a simple closure relationship between the evaporation rate and the degree of occupancy of the surface by the liquid. In addition to new insights into the surface phenomena, the results open up new prospects for improving the continuum models of the drying process. (c) 2017 American Institute of Chemical Engineers AIChE J, 64: 1435-1447, 2018