Convective heating of an initially partially saturated packed bed and the consequent surface and internal evaporation of the liquid is considered for cases where the temperature everywhere in the bed is below the saturation temperature at the local total pressure. In the first period where the liquid phase is continuous (funicular regime), the effect of surface tension nonuniformity on the liquid and gas phase flows is examined. The critical time (the time at which the surface saturation becomes equal to the immobile saturation) is found from the integration of the conservation equations. The effect of the absolute permeability heterogeneities on this critical time is examined, and it is shown that for normal distributions in porosity, the critical time increases over that for homogeneous permeabilities. The mass transfer rate during the evaporative front regime is also predicted by treating both the dry and the wet regions and the moving interface. An experiment is performed in which a 0.10 mm glass spheres-ethanol bed is convectively dried, and good agreement is found between the predicted and measured mass transfer rates, critical times, and surface temperatures.