A model of parallel capillaries with different diameters has been developed to explain back-diffusion experiments on four rather different graphites both impregnated and unimpregnated. The transport phenomenon has been taken as an interaction between diffusional and molecular flow on one hand, and viscous and slip flow on the other, to cover the whole range of diameter to mean-free-path ratios possible in graphite. It can be shown that only by assuming at least three bundles of capillaries with different diameters can these experiments be adequately explained. It is further possible to relate the material constants, the viscous flow component B0, and the slip flow component K0 to the pore-size distribution obtained. When we consider the complexity of porous capillaries in graphite, the agreement is found to be good, about 30%.