Dispersion remains, today, a highly topical subject. Our group has been interested in characterizing this phenomenon by pulsed-field-gradient NMR technique. Direct measurement of the dispersion coefficient can be done with a Pulsed Gradient Spin Echo (PGSE) sequence by assuming that the asymptotic regime is reached. In unsteady state, the propagator formalism is used. To better understand these measurements, the NMR experiment is modeled using a stochastic simulation (random walks) and compared with experimental results. The comparison is made for the simple case of Poiseuille flow in a circular tube (Taylor- Aris dispersion).