Present knowledge regarding the link between processes inside a reactor and its residence time distribution is still unsatisfying. As a contribution to close this gap, a mesoscopic cell model is discussed and validated. Special regard is given to possible error sources. Comparison of computed results with analytical residence time distributions and with the Taylor dispersion model show good agreement for ratios of cell size to rms distance of diffusion of 1.5-1.6 (one-dimensional case) and 1.3 (two-dimensional case). Model application to Poiseuille flow leads to a discussion of various dimensionless parameters. The transition in the form of residence time distributions from (P) over bare* = (v) over bard(2)/DmolL= 0.59 - 58.83 is discussed. Distributions in the case of (P) over bare* > 30 resemble the convection-only solution whereas cases with (P) over bare* > 3 have Gaussian distributions. Furthermore, distributions obtained from computation with radial diffusion only confirm that the neglect of axial diffusion leads to qualitatively correct results but reveal a quantitative disagreement in the residence time distribution's maxima.