The investigation of dispersion by microscopic simulations yields a lot of detailed information. To identify characteristic behaviours, it is useful to condense this information into a few effective parameters, which describe the transport process in the model geometry on a larger scale. For this purpose, a very simple two-velocity model has been developed, which models the transition from reversible to irreversible spreading of a tracer volume. It is shown that this model is very similar to Taylor-Aris dispersion and that it is quite suitable to approximate the time dependence of dispersion. The model is applied to characterize the effect of dead end pores on dispersion with a single correlation parameter. Up to Peclet numbers of about 500, ＇hold-up＇-dispersion similar to Taylor-Aris-dispersion is found. The simulations have been performed by the lattice Bhatnagar-Gross-Krook (BGK) method, which is a particular type of cellular automata and therefore allows an easy implementation of complicated geometries. The fully irreversible asymptotic dispersion is reached in an exponential process, the parameters of which can be identified by the two-velocity model after the mixing has noticeably begun. These are used to extrapolate the process which reduces the computational effort by about one order of magnitude.