We study sorption and transport processes in dry and wet (preadsorbed with CH2Br2) Vycor glass by combining small angle scattering and three-dimensional (3D) stochastic reconstruction methods. Three-phase systems of solid, condensate, and void space, are generated for the first time, by the combination of the above methods. The resulting 3D images can visualize the evolution of the adsorption process and show how sorption alters the pore space characteristics of the material. Desorption is modeled in this system with the additional employment of an invasion percolation algorithm to account for the hysteresis effect caused by the inaccessible regions of the porous matrix. It is found that desorption is simulated very well provided that the main mechanism for hysteresis depends only on the topology of the pore space and not on thermodynamic effects. Based on a random-walk procedure, Knudsen transport properties of the reconstructed images are also determined for different degrees of saturation, providing very good agreement with experimental relative permeability data. Thus, relative permeability reflects purely the pore accessibility properties of the material and may assist in discerning their exact contribution to the equilibrium sorption hysteresis loop.