Numerical simulations of transport in polydisperse oil-in-water emulsions were carried out for three situations in which the aqueous phase contained surfactant micelles: solubilization of a pure oil; Ostwald ripening of a pure oil; and compositional ripening of a mixed emulsion initially containing drops of two pure oils, only one of which was solubilized to a significant extent. Transport was assumed to be controlled by interfacial effects, not by diffusion of micelles in the aqueous phase. The results were compared with published data for changes in drop size distribution in hydrocarbon-in-oil emulsions stabilized by nonionic surfactants for each of the three phenomena. In some cases the published data were supplemented by measurements of interfacial tensions and solubilization rates of single drops of the same oils in solutions of the same nonionic surfactants. Excellent agreement between simulation results and the published data was found for the solubilization and compositional ripening cases with no adjustable parameters. Moreover, accounting for polydispersity was found to be important, i.e., agreement was sometimes not as good when the same transport mechanism was assumed but with a monodisperse distribution corresponding to average drop size. Although results for the Ostwald ripening case showed that interfacial effects and not diffusion controlled transport, confirming that the same mechanism of transport applied in all three cases, numerical agreement between simulations and experiment was not as good, probably because of additional transport between flocculated drops not accounted for in the theory.