The polymer matrix, divided in a number of cells in which the penetrant molecules can be sorbed and migrate, is considered. Each cell has been assigned an effective energy value that obeys a particular distribution. The effective diffusion coefficient and its concentration and temperature dependence are determined. The origin of sorbed penetrant mobility is studied. Using a delta-Dirac distribution for the site’s energetic values, the model is reduced in the appropriate limit (low pressure) to other formulations of the dual transport model. More general results, allowing the site’s energetic values to be drawn from a Gaussian distribution, are also given.