​We model porous media as two-dimensional networks of channels. As suspension flows through the network, particles clog channels. Assuming no flow through clogged channels, we determine an upper bound on the number of channels that clog and leave the network impervious. More precisely, the number of channels that clog does not exceed the number of faces of the multigraph associated with the network. In terms of d, the average coordination number of the network, the number of channels that clog does not exceed (1−2/d) of the total number of channels.