A dissipative particle dynamics computer simulation is used to investigate the ability of small oil molecules (hexane, dodecane, and octadecane) to control phase structures in nonionic surfactant water systems. The model is successfully tested against the experimental results for binary and ternary systems where the third components are "swelling" and "penetrating" oils. The experimentally observed phases present in such systems were successfully. modeled. In addition, the simulations show the locations of the oil molecules within the bilayer and the surfactant chain conformation. While the simulations confirm much of what is expected. from experiment and theoretical models, evidence is found for the terminal methyl end of the surfactant molecules being located slightly closer to the interfacial region than other groups in the same chain.