The axial dispersion in tubular reactors is frequently modeled by the dispersion model, which is an analytical solution under the assumption that the vessel dispersion number is sufficiently small. In this study, limits until which the analytical solution is valid are investigated by comparison with the numerical method. The results show that it is applied only if the vessel dispersion number is small enough and the entrance effect of the tracer is avoided. Therefore, an algorithm based on the numerical solution of the control equation of dispersion is proposed, which allows for higher vessel dispersion numbers.