An analysis of start-ups of PI-controlled CSTRs, based on the study of the time evolution of the divergence of the vector field defined by the reactor model differential equations, is presented. The divergence is linked to the dynamics of the an n-volume of initial conditions in the phase space. When the divergence is positive, nearby trajectories tend to diverge, implying that the reactor dynamics is sensitive to perturbations. So the divergence is effective for the study of the controllability characteristics of the reactor dynamics. The method, which is based on the complete non-linear model, is quite simple and synthetic portraits in the space of initial conditions can be obtained, for the controllability of start-ups. The effectiveness of the approach in the study of PI-controlled CSTRs is also discussed.