Industrial and natural systems involving the rapid flow of solid particulates often are characterized by particles with differences in size and/or density. Previous kinetic-theory-based models have been developed for such polydisperse systems, though they typically involve limiting assumptions. For example, an equipartition-of-energy assumption has been applied often, though previous experiments and simulations have shown that non-equipartition is not only prevalent, but also plays a role in species segregation for certain systems. In the current effort, a rigorous Chapman Enskog expansion is applied to the revised Enskog kinetic equation for a system of N species. This expansion is carried out about the homogeneous cooling state, and thus the resulting constitutive equations are applicable to a wide range of inelasticities. Furthermore, because the time scale associated with individual species is of the kinetic (fast) order, momentum and granular energy balances are only required for the mixture, not for individual species. The corresponding computational effort associated with solving the closed set of equations is expected to be lower than previous theories.