In this work, a new generalised model for transport properties is given, the theoretical background of some free-volume equations is revealed and the analysis of various free-volume expressions in the literature is presented. Firstly; we develop the free-volume equation for the self-diffusion coefficient, which embodies the hybrid principles of the real fluids, since it considers both the concepts of molecular free volume and activation energy. Secondly, it is shown that the relevant expressions presented in the literature are particular cases of our generalised equation. With this it is possible to clarify their validity and range of applicability, since the expressions arise by introducing approximations duly established in the fundamental model. Moreover, the relationship between free-volume expressions and the equations of state (EoS) of van der Waals (vdW) type is discussed. Some representative free-volume expressions are given and compared according to the effects of density, temperature and molecular shape. Following this comparison, some expressions are recommended.