The results of ongoing efforts by this group to model the transport of asphaltene molecules through model membranes are presented. A model is described which aims to capture the effect of the polydisperse nature of asphaltene molecules on their transport properties. The asphaltene structure is generated stochastically using Monte Carlo techniques. Individual asphaltene molecules are approximated as spheroids for the purpose of calculating their hindered diffusivities. Continuum hydrodynamic theories and boundary element methods are used to calculate the diffusion coefficients. A number of analytical expressions, scaling relationships, and approximations utilized in the literature are evaluated.