Results of a three-dimensional pore network simulation of drying under constant external conditions are reported. It is shown that the pore network drying model capture specific features of drying of capillary porous media such that the phenomenon of dry patches and the occurrence of a constant rate period (CRP). These phenomena are explained as consequences of the fractal invasion percolation patterns that characterize drying when the capillary forces dominate. The evolution of the liquid phase structure within the pore network during drying is studied and the process of fragmentation of the liquid phase into isolated clusters is analysed. The various periods of the drying curve are analysed from the evolution of the liquid phase distribution within the sample.